An Introduction To Sato S Hyperfunctions

Author : Mitsuo Morimoto
Publisher : American Mathematical Soc.
Page : 292 pages
File Size : 54,6 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 082188767X

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An Introduction to Sato's Hyperfunctions by Mitsuo Morimoto Pdf

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.

Author : Urs Graf
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 41,7 Mb
Release : 2010-03-12
Category : Mathematics
ISBN : 9783034604079

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Introduction to Hyperfunctions and Their Integral Transforms by Urs Graf Pdf

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.

Author : A. Kaneko
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 44,8 Mb
Release : 1989-02-28
Category : Mathematics
ISBN : 9027728372

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Introduction to the Theory of Hyperfunctions by A. Kaneko Pdf

Author : M. Hazewinkel
Publisher : Springer
Page : 952 pages
File Size : 49,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489937933

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Encyclopaedia of Mathematics by M. Hazewinkel Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 44,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959972

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Sabir Umarov
Publisher : Springer
Page : 434 pages
File Size : 47,9 Mb
Release : 2015-08-18
Category : Mathematics
ISBN : 9783319207711

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Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols by Sabir Umarov Pdf

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

Author : Hikosaburo Komatsu
Publisher : Springer
Page : 536 pages
File Size : 48,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385066

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Hyperfunctions and Pseudo-Differential Equations by Hikosaburo Komatsu Pdf

Author : Henrik Schlichtkrull
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461252986

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Hyperfunctions and Harmonic Analysis on Symmetric Spaces by Henrik Schlichtkrull Pdf

This book gives an introductory exposition of the theory of hyperfunctions and regular singularities. 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.

Author : Takahiro Kawai,Keiko Fujita,Ky?to Daigaku. S?ri Kaiseki Kenky?jo
Publisher : World Scientific
Page : 339 pages
File Size : 53,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9789812381613

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Microlocal Analysis and Complex Fourier Analysis by Takahiro Kawai,Keiko Fujita,Ky?to Daigaku. S?ri Kaiseki Kenky?jo Pdf

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 ?Prospects of Generalized Functions? (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.

Author : Karl E. Gustafson
Publisher : Courier Corporation
Page : 500 pages
File Size : 48,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486140872

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Introduction to Partial Differential Equations and Hilbert Space Methods by Karl E. Gustafson Pdf

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

Author : Isao Imai
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 46,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401125482

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Applied Hyperfunction Theory by Isao Imai Pdf

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.

Author : Victor Guillemin,Masaki Kashiwara,Takahiro Kawai
Publisher : Princeton University Press
Page : 148 pages
File Size : 48,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881574

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Seminar on Micro-Local Analysis. (AM-93), Volume 93 by Victor Guillemin,Masaki Kashiwara,Takahiro Kawai Pdf

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.

Author : Paulo Cordaro,François Treves
Publisher : Princeton University Press
Page : 378 pages
File Size : 51,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882564

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Hyperfunctions on Hypo-Analytic Manifolds (AM-136), Volume 136 by Paulo Cordaro,François Treves Pdf

In the first two chapters of this book, the reader will find a complete and systematic exposition of the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in real space. The book provides precise definitions of the hypo-analytic wave-front set and of the Fourier-Bros-Iagolnitzer transform of a hyperfunction. These are used to prove a very general version of the famed Theorem of the Edge of the Wedge. The last two chapters define the hyperfunction solutions on a general (smooth) hypo-analytic manifold, of which particular examples are the real analytic manifolds and the embedded CR manifolds. The main results here are the invariance of the spaces of hyperfunction solutions and the transversal smoothness of every hyperfunction solution. From this follows the uniqueness of solutions in the Cauchy problem with initial data on a maximally real submanifold, and the fact that the support of any solution is the union of orbits of the structure.

Author : Michael Hitrik,Dmitry Tamarkin,Boris Tsygan,Steve Zelditch
Publisher : Springer
Page : 654 pages
File Size : 50,9 Mb
Release : 2018-12-19
Category : Mathematics
ISBN : 9783030015886

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Algebraic and Analytic Microlocal Analysis by Michael Hitrik,Dmitry Tamarkin,Boris Tsygan,Steve Zelditch Pdf

This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.

Author : Joji Kajiwara,Zhong Li,Kwang Ho Shon
Publisher : CRC Press
Page : 674 pages
File Size : 48,9 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9780429530005

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Finite or Infinite Dimensional Complex Analysis by Joji Kajiwara,Zhong Li,Kwang Ho Shon Pdf

This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.