Introduction To The Theory Of Hyperfunctions

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Introduction To The Theory Of Hyperfunctions
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Author : A. Kaneko
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-02-28
Introduction To The Theory Of Hyperfunctions written by A. Kaneko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-02-28 with Mathematics categories.
An Introduction To Sato S Hyperfunctions
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Author : Mitsuo Morimoto
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
An Introduction To Sato S Hyperfunctions written by Mitsuo Morimoto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research.
Introduction To Hyperfunctions And Their Integral Transforms
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Author : Urs Graf
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-28
Introduction To Hyperfunctions And Their Integral Transforms written by Urs Graf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-28 with Mathematics categories.
This textbook presents an introduction to the subject of generalized functions and their integral transforms by an approach based on the theory of functions of one complex variable. It includes many concrete examples.
Microlocal Analysis And Complex Fourier Analysis
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Author : Keiko Fujita
language : en
Publisher: World Scientific
Release Date : 2002
Microlocal Analysis And Complex Fourier Analysis written by Keiko Fujita and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book is a collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics. Most of the papers originate from the talks given at the conference OC Prospects of Generalized FunctionsOCO (in November, 2001 at RIMS, Kyoto). Reflecting the fact that the papers, except M Morimoto''s one, are dedicated to Mitsuo Morimoto, the subjects considered in this book are interdisciplinary, just as Morimoto''s works are. The historical backgrounds of the subjects are also discussed in depth in some contributions. Thus, this book should be valuable not only to the specialists in the fields, but also to those who are interested in the history of modern mathematics such as distributions and hyperfunctions."
Applied Hyperfunction Theory
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Author : Isao Imai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Applied Hyperfunction Theory written by Isao Imai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Generalized functions are now widely recognized as important mathematical tools for engineers and physicists. But they are considered to be inaccessible for non-specialists. To remedy this situation, this book gives an intelligible exposition of generalized functions based on Sato's hyperfunction, which is essentially the `boundary value of analytic functions'. An intuitive image -- hyperfunction = vortex layer -- is adopted, and only an elementary knowledge of complex function theory is assumed. The treatment is entirely self-contained. The first part of the book gives a detailed account of fundamental operations such as the four arithmetical operations applicable to hyperfunctions, namely differentiation, integration, and convolution, as well as Fourier transform. Fourier series are seen to be nothing but periodic hyperfunctions. In the second part, based on the general theory, the Hilbert transform and Poisson-Schwarz integral formula are treated and their application to integral equations is studied. A great number of formulas obtained in the course of treatment are summarized as tables in the appendix. In particular, those concerning convolution, the Hilbert transform and Fourier transform contain much new material. For mathematicians, mathematical physicists and engineers whose work involves generalized functions.
Hyperfunctions And Pseudo Differential Equations
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Author : Hikosaburo Komatsu
language : en
Publisher: Springer
Release Date : 2006-11-15
Hyperfunctions And Pseudo Differential Equations written by Hikosaburo Komatsu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Hyperfunctions And Harmonic Analysis On Symmetric Spaces
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Author : Henrik Schlichtkrull
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hyperfunctions And Harmonic Analysis On Symmetric Spaces written by Henrik Schlichtkrull and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions. The technique has had several important applications in harmonic analysis for symmetric spaces. This book gives an introductory exposition of the theory of hyperfunctions and regular singularities, and on this basis it treats two major applications to harmonic analysis. The first is to the proof of Helgason’s conjecture, due to Kashiwara et al., which represents eigenfunctions on Riemannian symmetric spaces as Poisson integrals of their hyperfunction boundary values. A generalization of this result involving the full boundary of the space is also given. The second topic is the construction of discrete series for semisimple symmetric spaces, with an unpublished proof, due to Oshima, of a conjecture of Flensted-Jensen. This first English introduction to hyperfunctions brings readers to the forefront of research in the theory of harmonic analysis on symmetric spaces. A substantial bibliography is also included. This volume is based on a paper which was awarded the 1983 University of Copenhagen Gold Medal Prize.
Seminar On Micro Local Analysis
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Author : Victor Guillemin
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Seminar On Micro Local Analysis written by Victor Guillemin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.
Classical Microlocal Analysis In The Space Of Hyperfunctions
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Author : Seiichiro Wakabayashi
language : en
Publisher: Springer
Release Date : 2007-05-06
Classical Microlocal Analysis In The Space Of Hyperfunctions written by Seiichiro Wakabayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.
Pseudo Differential Operators Analysis Applications And Computations
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Author : Luigi Rodino
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-13
Pseudo Differential Operators Analysis Applications And Computations written by Luigi Rodino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-13 with Mathematics categories.
This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics”, “Modern Trends in Pseudo-Differential Operators”, “New Developments in Pseudo-Differential Operators” and “Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations” published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.