A Guide to Spectral Theory

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Publisher : Springer Nature
ISBN 13 : 3030674622
Total Pages : 258 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis A Guide to Spectral Theory by : Christophe Cheverry

Download or read book A Guide to Spectral Theory written by Christophe Cheverry and published by Springer Nature. This book was released on 2021-05-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

Spectral Theory and Differential Operators

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Publisher : Oxford University Press
ISBN 13 : 0198812051
Total Pages : 610 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Spectral Theory and Differential Operators by : David Eric Edmunds

Download or read book Spectral Theory and Differential Operators written by David Eric Edmunds and published by Oxford University Press. This book was released on 2018 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.--

A User's Guide to Spectral Sequences

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Publisher : Cambridge University Press
ISBN 13 : 0521567599
Total Pages : 579 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis A User's Guide to Spectral Sequences by : John McCleary

Download or read book A User's Guide to Spectral Sequences written by John McCleary and published by Cambridge University Press. This book was released on 2001 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Spectral Mapping Theorems

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Publisher : Springer
ISBN 13 : 3319056484
Total Pages : 132 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Spectral Mapping Theorems by : Robin Harte

Download or read book Spectral Mapping Theorems written by Robin Harte and published by Springer. This book was released on 2014-04-29 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.

Spectral Theory of Self-Adjoint Operators in Hilbert Space

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Publisher : Springer Science & Business Media
ISBN 13 : 9400945868
Total Pages : 316 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Spectral Theory of Self-Adjoint Operators in Hilbert Space by : Michael Sh. Birman

Download or read book Spectral Theory of Self-Adjoint Operators in Hilbert Space written by Michael Sh. Birman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Functional Analysis, Spectral Theory, and Applications

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Publisher : Springer
ISBN 13 : 3319585401
Total Pages : 614 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Functional Analysis, Spectral Theory, and Applications by : Manfred Einsiedler

Download or read book Functional Analysis, Spectral Theory, and Applications written by Manfred Einsiedler and published by Springer. This book was released on 2017-11-21 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.

A Guide to Functional Analysis

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Publisher : MAA
ISBN 13 : 0883853574
Total Pages : 151 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis A Guide to Functional Analysis by : Steven G. Krantz

Download or read book A Guide to Functional Analysis written by Steven G. Krantz and published by MAA. This book was released on 2013-06-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.

Spectral Theory of Random Schrödinger Operators

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Publisher : Springer Science & Business Media
ISBN 13 : 1461244889
Total Pages : 611 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Spectral Theory of Random Schrödinger Operators by : R. Carmona

Download or read book Spectral Theory of Random Schrödinger Operators written by R. Carmona and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.

Inverse Spectral and Scattering Theory

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Publisher : Springer Nature
ISBN 13 : 9811581991
Total Pages : 130 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Inverse Spectral and Scattering Theory by : Hiroshi Isozaki

Download or read book Inverse Spectral and Scattering Theory written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2020-09-26 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical science. These practical problems boil down to the mathematical question in which one tries to recover the operator (coefficients) or the domain (manifolds) from spectral data. The characteristic properties of the operators in question are often reduced to those of Schrödinger operators. We start from the 1-dimensional theory to observe the main features of inverse spectral problems and then proceed to multi-dimensions. The first milestone is the Borg–Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem as well as the difference between 1-dimension and multi-dimension. The main theme is the inverse scattering, in which the spectral data is Heisenberg’s S-matrix defined through the observation of the asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30 years by using the Faddeev–Green function or the complex geometrical optics solution by Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-matrix of one fixed energy. One can also prove the equivalence of the knowledge of S-matrix and that of the Dirichlet-to-Neumann map for boundary value problems in bounded domains. We apply this idea also to the Dirac equation, the Maxwell equation, and discrete Schrödinger operators on perturbed lattices. Our final topic is the boundary control method introduced by Belishev and Kurylev, which is for the moment the only systematic method for the reconstruction of the Riemannian metric from the boundary observation, which we apply to the inverse scattering on non-compact manifolds. We stress that this book focuses on the lucid exposition of these problems and mathematical backgrounds by explaining the basic knowledge of functional analysis and spectral theory, omitting the technical details in order to make the book accessible to graduate students as an introduction to partial differential equations (PDEs) and functional analysis.

Spectral Analysis of Signals

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Publisher : Springer Nature
ISBN 13 : 3031025253
Total Pages : 99 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Spectral Analysis of Signals by : Yanwei Wang

Download or read book Spectral Analysis of Signals written by Yanwei Wang and published by Springer Nature. This book was released on 2022-05-31 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral estimation is important in many fields including astronomy, meteorology, seismology, communications, economics, speech analysis, medical imaging, radar, sonar, and underwater acoustics. Most existing spectral estimation algorithms are devised for uniformly sampled complete-data sequences. However, the spectral estimation for data sequences with missing samples is also important in many applications ranging from astronomical time series analysis to synthetic aperture radar imaging with angular diversity. For spectral estimation in the missing-data case, the challenge is how to extend the existing spectral estimation techniques to deal with these missing-data samples. Recently, nonparametric adaptive filtering based techniques have been developed successfully for various missing-data problems. Collectively, these algorithms provide a comprehensive toolset for the missing-data problem based exclusively on the nonparametric adaptive filter-bank approaches, which are robust and accurate, and can provide high resolution and low sidelobes. In this book, we present these algorithms for both one-dimensional and two-dimensional spectral estimation problems.

Introduction to Hilbert Space and the Theory of Spectral Multiplicity

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Publisher : Courier Dover Publications
ISBN 13 : 048682683X
Total Pages : 129 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Introduction to Hilbert Space and the Theory of Spectral Multiplicity by : Paul R. Halmos

Download or read book Introduction to Hilbert Space and the Theory of Spectral Multiplicity written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-11-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

Digital Spectral Analysis

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Publisher : Courier Dover Publications
ISBN 13 : 048678052X
Total Pages : 435 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Digital Spectral Analysis by : S. Lawrence Marple, Jr.

Download or read book Digital Spectral Analysis written by S. Lawrence Marple, Jr. and published by Courier Dover Publications. This book was released on 2019-03-20 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digital Spectral Analysis offers a broad perspective of spectral estimation techniques and their implementation. Coverage includes spectral estimation of discrete-time or discrete-space sequences derived by sampling continuous-time or continuous-space signals. The treatment emphasizes the behavior of each spectral estimator for short data records and provides over 40 techniques described and available as implemented MATLAB functions. In addition to summarizing classical spectral estimation, this text provides theoretical background and review material in linear systems, Fourier transforms, matrix algebra, random processes, and statistics. Topics include Prony's method, parametric methods, the minimum variance method, eigenanalysis-based estimators, multichannel methods, and two-dimensional methods. Suitable for advanced undergraduates and graduate students of electrical engineering — and for scientific use in the signal processing application community outside of universities — the treatment's prerequisites include some knowledge of discrete-time linear system and transform theory, introductory probability and statistics, and linear algebra. 1987 edition.

Gaussian Processes, Function Theory, and the Inverse Spectral Problem

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Publisher : Courier Corporation
ISBN 13 : 048646279X
Total Pages : 354 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Gaussian Processes, Function Theory, and the Inverse Spectral Problem by : Harry Dym

Download or read book Gaussian Processes, Function Theory, and the Inverse Spectral Problem written by Harry Dym and published by Courier Corporation. This book was released on 2008-01-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral functions. It addresses the relationship between the past and the future of a real, one-dimensional, stationary Gaussian process. 1976 edition.

The Spectral Analysis of Time Series

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Publisher : Academic Press
ISBN 13 : 1483218546
Total Pages : 382 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Spectral Analysis of Time Series by : L. H. Koopmans

Download or read book The Spectral Analysis of Time Series written by L. H. Koopmans and published by Academic Press. This book was released on 2014-05-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.

Chebyshev and Fourier Spectral Methods

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Publisher : Courier Corporation
ISBN 13 : 0486411834
Total Pages : 690 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd

Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Scala: Guide for Data Science Professionals

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Publisher : Packt Publishing Ltd
ISBN 13 : 1787281035
Total Pages : 1101 pages
Book Rating : 4.7/5 (872 download)

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Book Synopsis Scala: Guide for Data Science Professionals by : Pascal Bugnion

Download or read book Scala: Guide for Data Science Professionals written by Pascal Bugnion and published by Packt Publishing Ltd. This book was released on 2017-02-24 with total page 1101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scala will be a valuable tool to have on hand during your data science journey for everything from data cleaning to cutting-edge machine learning About This Book Build data science and data engineering solutions with ease An in-depth look at each stage of the data analysis process — from reading and collecting data to distributed analytics Explore a broad variety of data processing, machine learning, and genetic algorithms through diagrams, mathematical formulations, and source code Who This Book Is For This learning path is perfect for those who are comfortable with Scala programming and now want to enter the field of data science. Some knowledge of statistics is expected. What You Will Learn Transfer and filter tabular data to extract features for machine learning Read, clean, transform, and write data to both SQL and NoSQL databases Create Scala web applications that couple with JavaScript libraries such as D3 to create compelling interactive visualizations Load data from HDFS and HIVE with ease Run streaming and graph analytics in Spark for exploratory analysis Bundle and scale up Spark jobs by deploying them into a variety of cluster managers Build dynamic workflows for scientific computing Leverage open source libraries to extract patterns from time series Master probabilistic models for sequential data In Detail Scala is especially good for analyzing large sets of data as the scale of the task doesn't have any significant impact on performance. Scala's powerful functional libraries can interact with databases and build scalable frameworks — resulting in the creation of robust data pipelines. The first module introduces you to Scala libraries to ingest, store, manipulate, process, and visualize data. Using real world examples, you will learn how to design scalable architecture to process and model data — starting from simple concurrency constructs and progressing to actor systems and Apache Spark. After this, you will also learn how to build interactive visualizations with web frameworks. Once you have become familiar with all the tasks involved in data science, you will explore data analytics with Scala in the second module. You'll see how Scala can be used to make sense of data through easy to follow recipes. You will learn about Bokeh bindings for exploratory data analysis and quintessential machine learning with algorithms with Spark ML library. You'll get a sufficient understanding of Spark streaming, machine learning for streaming data, and Spark graphX. Armed with a firm understanding of data analysis, you will be ready to explore the most cutting-edge aspect of data science — machine learning. The final module teaches you the A to Z of machine learning with Scala. You'll explore Scala for dependency injections and implicits, which are used to write machine learning algorithms. You'll also explore machine learning topics such as clustering, dimentionality reduction, Naive Bayes, Regression models, SVMs, neural networks, and more. This learning path combines some of the best that Packt has to offer into one complete, curated package. It includes content from the following Packt products: Scala for Data Science, Pascal Bugnion Scala Data Analysis Cookbook, Arun Manivannan Scala for Machine Learning, Patrick R. Nicolas Style and approach A complete package with all the information necessary to start building useful data engineering and data science solutions straight away. It contains a diverse set of recipes that cover the full spectrum of interesting data analysis tasks and will help you revolutionize your data analysis skills using Scala.

Spectral Theory and Its Applications

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Publisher : Cambridge University Press
ISBN 13 : 110703230X
Total Pages : 263 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Spectral Theory and Its Applications by : Bernard Helffer

Download or read book Spectral Theory and Its Applications written by Bernard Helffer and published by Cambridge University Press. This book was released on 2013-01-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.