Functional Operators

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Advanced R

Author : Hadley Wickham
Publisher : CRC Press
ISBN 13 : 1498759807
Total Pages : 669 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Advanced R by : Hadley Wickham

Download or read book Advanced R written by Hadley Wickham and published by CRC Press. This book was released on 2015-09-15 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.

The Functional Calculus for Sectorial Operators

Author : Markus Haase
Publisher : Springer Science & Business Media
ISBN 13 : 3764376988
Total Pages : 399 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis The Functional Calculus for Sectorial Operators by : Markus Haase

Download or read book The Functional Calculus for Sectorial Operators written by Markus Haase and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.

Functional Equations with Causal Operators

Author : C. Corduneanu
Publisher : CRC Press
ISBN 13 : 020316637X
Total Pages : 185 pages
Book Rating : 4.2/5 (31 download)

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Book Synopsis Functional Equations with Causal Operators by : C. Corduneanu

Download or read book Functional Equations with Causal Operators written by C. Corduneanu and published by CRC Press. This book was released on 2002-09-05 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

Author : Tailen Hsing
Publisher : John Wiley & Sons
ISBN 13 : 0470016914
Total Pages : 363 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by : Tailen Hsing

Download or read book Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators written by Tailen Hsing and published by John Wiley & Sons. This book was released on 2015-05-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Functional Analysis

Author : Theo Bühler
Publisher : American Mathematical Soc.
ISBN 13 : 147044190X
Total Pages : 482 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Functional Analysis by : Theo Bühler

Download or read book Functional Analysis written by Theo Bühler and published by American Mathematical Soc.. This book was released on 2018-08-08 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.

Optimal Domain and Integral Extension of Operators

Author : S. Okada
Publisher : Springer Science & Business Media
ISBN 13 : 3764386487
Total Pages : 406 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Optimal Domain and Integral Extension of Operators by : S. Okada

Download or read book Optimal Domain and Integral Extension of Operators written by S. Okada and published by Springer Science & Business Media. This book was released on 2008-09-09 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.

Composition Operators

Author : Joel H. Shapiro
Publisher : Springer Science & Business Media
ISBN 13 : 1461208874
Total Pages : 229 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Composition Operators by : Joel H. Shapiro

Download or read book Composition Operators written by Joel H. Shapiro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean ings, and bestows upon functional analysis an intriguing class of concrete linear operators. Best of all, the subject can be appreciated by anyone with an interest in function theory or functional analysis, and a background roughly equivalent to the following twelve chapters of Rudin's textbook Real and Complex Analysis [Rdn '87]: Chapters 1-7 (measure and integra tion, LP spaces, basic Hilbert and Banach space theory), and 10-14 (basic function theory through the Riemann Mapping Theorem). In this book I introduce the reader to both the theory of composition operators, and the classical results that form its infrastructure. I develop the subject in a way that emphasizes its geometric content, staying as much as possible within the prerequisites set out in the twelve fundamental chapters of Rudin's book. Although much of the material on operators is quite recent, this book is not intended to be an exhaustive survey. It is, quite simply, an invitation to join in the fun. The story goes something like this.

Function Spaces, Differential Operators and Nonlinear Analysis

Author : Dorothee Haroske
Publisher : Springer Science & Business Media
ISBN 13 : 9783764369354
Total Pages : 494 pages
Book Rating : 4.3/5 (693 download)

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Book Synopsis Function Spaces, Differential Operators and Nonlinear Analysis by : Dorothee Haroske

Download or read book Function Spaces, Differential Operators and Nonlinear Analysis written by Dorothee Haroske and published by Springer Science & Business Media. This book was released on 2003-02-24 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.

Functional Operators: Measures and integrals

Author : John Von Neumann
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Functional Operators: Measures and integrals by : John Von Neumann

Download or read book Functional Operators: Measures and integrals written by John Von Neumann and published by . This book was released on 1950 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces

Author : L. Molnár
Publisher : Springer
ISBN 13 : 3540399461
Total Pages : 243 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces by : L. Molnár

Download or read book Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces written by L. Molnár and published by Springer. This book was released on 2006-11-15 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The territory of preserver problems has grown continuously within linear analysis. This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is placed on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.

Operators, Semigroups, Algebras and Function Theory

Author : Yemon Choi
Publisher : Springer Nature
ISBN 13 : 3031380207
Total Pages : 262 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Operators, Semigroups, Algebras and Function Theory by : Yemon Choi

Download or read book Operators, Semigroups, Algebras and Function Theory written by Yemon Choi and published by Springer Nature. This book was released on 2023-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

R in a Nutshell

Author : Joseph Adler
Publisher : "O'Reilly Media, Inc."
ISBN 13 : 144931208X
Total Pages : 723 pages
Book Rating : 4.4/5 (493 download)

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Book Synopsis R in a Nutshell by : Joseph Adler

Download or read book R in a Nutshell written by Joseph Adler and published by "O'Reilly Media, Inc.". This book was released on 2012-10-09 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a guide to the R computer language, covering such topics as the user interface, packages, syntax, objects, functions, object-oriented programming, data sets, lattice graphics, regression models, and bioconductor.

Operator Theory, Functional Analysis and Applications

Author : M. Amélia Bastos
Publisher : Birkhäuser
ISBN 13 : 9783030519445
Total Pages : 657 pages
Book Rating : 4.5/5 (194 download)

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Book Synopsis Operator Theory, Functional Analysis and Applications by : M. Amélia Bastos

Download or read book Operator Theory, Functional Analysis and Applications written by M. Amélia Bastos and published by Birkhäuser. This book was released on 2021-04-01 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Narrow Operators on Function Spaces and Vector Lattices

Author : Mikhail Popov
Publisher : Walter de Gruyter
ISBN 13 : 3110263343
Total Pages : 336 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Narrow Operators on Function Spaces and Vector Lattices by : Mikhail Popov

Download or read book Narrow Operators on Function Spaces and Vector Lattices written by Mikhail Popov and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.

Composition Operators on Function Spaces

Author : R.K. Singh
Publisher : Elsevier
ISBN 13 : 0080872905
Total Pages : 327 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Composition Operators on Function Spaces by : R.K. Singh

Download or read book Composition Operators on Function Spaces written by R.K. Singh and published by Elsevier. This book was released on 1993-11-03 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics.After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed.This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.

Hardy Operators, Function Spaces and Embeddings

Author : David E. Edmunds
Publisher : Springer Science & Business Media
ISBN 13 : 9783540219729
Total Pages : 352 pages
Book Rating : 4.2/5 (197 download)

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Book Synopsis Hardy Operators, Function Spaces and Embeddings by : David E. Edmunds

Download or read book Hardy Operators, Function Spaces and Embeddings written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2004-07-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.

Integral Operators in Non-Standard Function Spaces

Author : Vakhtang Kokilashvili
Publisher : Birkhäuser
ISBN 13 : 3319210157
Total Pages : 585 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Integral Operators in Non-Standard Function Spaces by : Vakhtang Kokilashvili

Download or read book Integral Operators in Non-Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.