Hangzhou Lectures On Eigenfunctions Of The Laplacian Am 188

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Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Author : Christopher D. Sogge
Publisher : Princeton University Press
ISBN 13 : 0691160783
Total Pages : 205 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) by : Christopher D. Sogge

Download or read book Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) written by Christopher D. Sogge and published by Princeton University Press. This book was released on 2014-03-10 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.

Hangzhou Lectures on Eigenfunctions of the Laplacian

Author : Christopher Donald Sogge
Publisher :
ISBN 13 : 9780691160757
Total Pages : 193 pages
Book Rating : 4.1/5 (67 download)

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Book Synopsis Hangzhou Lectures on Eigenfunctions of the Laplacian by : Christopher Donald Sogge

Download or read book Hangzhou Lectures on Eigenfunctions of the Laplacian written by Christopher Donald Sogge and published by . This book was released on 1940 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Microlocal Analysis, Sharp Spectral Asymptotics and Applications II

Author : Victor Ivrii
Publisher : Springer Nature
ISBN 13 : 3030305414
Total Pages : 525 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications II by : Victor Ivrii

Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications II written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-11 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications III

Author : Victor Ivrii
Publisher : Springer Nature
ISBN 13 : 3030305376
Total Pages : 729 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications III by : Victor Ivrii

Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications III written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-12 with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV

Author : Victor Ivrii
Publisher : Springer Nature
ISBN 13 : 3030305457
Total Pages : 714 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV by : Victor Ivrii

Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-11 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications I

Author : Victor Ivrii
Publisher : Springer Nature
ISBN 13 : 3030305570
Total Pages : 889 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications I by : Victor Ivrii

Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications I written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-12 with total page 889 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications V

Author : Victor Ivrii
Publisher : Springer Nature
ISBN 13 : 3030305619
Total Pages : 739 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications V by : Victor Ivrii

Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications V written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-13 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.

Tools and Problems in Partial Differential Equations

Author : Thomas Alazard
Publisher : Springer Nature
ISBN 13 : 3030502848
Total Pages : 357 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Tools and Problems in Partial Differential Equations by : Thomas Alazard

Download or read book Tools and Problems in Partial Differential Equations written by Thomas Alazard and published by Springer Nature. This book was released on 2020-10-19 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations. Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory. Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject.

Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

Author : Nail A Gumerov
Publisher : Elsevier
ISBN 13 : 0080531598
Total Pages : 551 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Fast Multipole Methods for the Helmholtz Equation in Three Dimensions by : Nail A Gumerov

Download or read book Fast Multipole Methods for the Helmholtz Equation in Three Dimensions written by Nail A Gumerov and published by Elsevier. This book was released on 2005-01-27 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians. The Only book that provides comprehensive coverage of this topic in one location Presents a review of the basic theory of expansions of the Helmholtz equation solutions Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation

Eigenfunctions of the Laplacian on a Riemannian Manifold

Author : Steve Zelditch
Publisher : American Mathematical Soc.
ISBN 13 : 1470410370
Total Pages : 410 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Eigenfunctions of the Laplacian on a Riemannian Manifold by : Steve Zelditch

Download or read book Eigenfunctions of the Laplacian on a Riemannian Manifold written by Steve Zelditch and published by American Mathematical Soc.. This book was released on 2017-12-12 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Eigenvalues, Inequalities, and Ergodic Theory

Author : Mu-Fa Chen
Publisher : Springer Science & Business Media
ISBN 13 : 1846281237
Total Pages : 239 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Eigenvalues, Inequalities, and Ergodic Theory by : Mu-Fa Chen

Download or read book Eigenvalues, Inequalities, and Ergodic Theory written by Mu-Fa Chen and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use

Intelligent Computing Techniques for Smart Energy Systems

Author : Akhtar Kalam
Publisher : Springer Nature
ISBN 13 : 9811502145
Total Pages : 1011 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Intelligent Computing Techniques for Smart Energy Systems by : Akhtar Kalam

Download or read book Intelligent Computing Techniques for Smart Energy Systems written by Akhtar Kalam and published by Springer Nature. This book was released on 2019-12-16 with total page 1011 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book compiles the research works related to smart solutions concept in context to smart energy systems, maintaining electrical grid discipline and resiliency, computational collective intelligence consisted of interaction between smart devices, smart environments and smart interactions, as well as information technology support for such areas. It includes high-quality papers presented in the International Conference on Intelligent Computing Techniques for Smart Energy Systems organized by Manipal University Jaipur. This book will motivate scholars to work in these areas. The book also prophesies their approach to be used for the business and the humanitarian technology development as research proposal to various government organizations for funding approval.

Proceedings of the 5th International Conference on Electrical Engineering and Automatic Control

Author : Bo Huang
Publisher : Springer
ISBN 13 : 9783662487662
Total Pages : 0 pages
Book Rating : 4.4/5 (876 download)

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Book Synopsis Proceedings of the 5th International Conference on Electrical Engineering and Automatic Control by : Bo Huang

Download or read book Proceedings of the 5th International Conference on Electrical Engineering and Automatic Control written by Bo Huang and published by Springer. This book was released on 2016-07-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the basis of instrument electrical and automatic control system, the 5th International Conference on Electrical Engineering and Automatic Control (CEEAC) was established at the crossroads of information technology and control technology, and seeks to effectively apply information technology to a sweeping trend that views control as the core of intelligent manufacturing and life. This book takes a look forward into advanced manufacturing development, an area shaped by intelligent manufacturing. It highlights the application and promotion of process control represented by traditional industries, such as the steel industry and petrochemical industry; the technical equipment and system cooperative control represented by robot technology and multi-axis CNC; and the control and support of emerging process technologies represented by laser melting and stacking, as well as the emerging industry represented by sustainable and intelligent life. The book places particular emphasis on the micro-segments field, such as intelligent micro-grids, new energy vehicles, and the Internet of Things.

Fourier Integrals in Classical Analysis

Author : Christopher D. Sogge
Publisher : Cambridge University Press
ISBN 13 : 1107120071
Total Pages : 349 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Fourier Integrals in Classical Analysis by : Christopher D. Sogge

Download or read book Fourier Integrals in Classical Analysis written by Christopher D. Sogge and published by Cambridge University Press. This book was released on 2017-04-27 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.

Arbeitstagung Bonn, 1984

Author : Friedrich Hirzebruch
Publisher : Springer
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Arbeitstagung Bonn, 1984 by : Friedrich Hirzebruch

Download or read book Arbeitstagung Bonn, 1984 written by Friedrich Hirzebruch and published by Springer. This book was released on 1985 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Neural Networks and Statistical Learning

Author : Ke-Lin Du
Publisher : Springer Science & Business Media
ISBN 13 : 1447155718
Total Pages : 834 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Neural Networks and Statistical Learning by : Ke-Lin Du

Download or read book Neural Networks and Statistical Learning written by Ke-Lin Du and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a broad but in-depth introduction to neural network and machine learning in a statistical framework, this book provides a single, comprehensive resource for study and further research. All the major popular neural network models and statistical learning approaches are covered with examples and exercises in every chapter to develop a practical working understanding of the content. Each of the twenty-five chapters includes state-of-the-art descriptions and important research results on the respective topics. The broad coverage includes the multilayer perceptron, the Hopfield network, associative memory models, clustering models and algorithms, the radial basis function network, recurrent neural networks, principal component analysis, nonnegative matrix factorization, independent component analysis, discriminant analysis, support vector machines, kernel methods, reinforcement learning, probabilistic and Bayesian networks, data fusion and ensemble learning, fuzzy sets and logic, neurofuzzy models, hardware implementations, and some machine learning topics. Applications to biometric/bioinformatics and data mining are also included. Focusing on the prominent accomplishments and their practical aspects, academic and technical staff, graduate students and researchers will find that this provides a solid foundation and encompassing reference for the fields of neural networks, pattern recognition, signal processing, machine learning, computational intelligence, and data mining.

Mathematics of Wave Phenomena

Author : Willy Dörfler
Publisher : Springer Nature
ISBN 13 : 3030471748
Total Pages : 330 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Mathematics of Wave Phenomena by : Willy Dörfler

Download or read book Mathematics of Wave Phenomena written by Willy Dörfler and published by Springer Nature. This book was released on 2020-10-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.