Introduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational Approach by Urs GrafIntroduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational Approach by Urs Graf

Introduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational Approach

byUrs Graf

Hardcover | March 12, 2010

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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.

Title:Introduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational ApproachFormat:HardcoverDimensions:432 pagesPublished:March 12, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034604076

ISBN - 13:9783034604079

Reviews

Table of Contents

Preface.- 1 Introduction to Hyperfunctions.- 2 Analytic Properties.- 3 Laplace Transforms.- 4 Fourier Transforms.- 5 Hilbert Transforms.- 6 Mellin Transforms.- 7 Hankel Transforms.- A Complements.- B Tables.- List of Symbols.- Bibliography. Index.

Editorial Reviews

From the reviews:"The intended audience of the book is advanced undergraduate students, graduate students, and research professionals in mathematical sciences. The book can serve as a research reference or a supplement to courses or seminars. . this book provides an excellent presentation of integral transforms of hyperfunctions with examples of applications to integral equations and ordinary and partial differential equations. . would be successful as a senior undergraduate- or graduate-level text in mathematics, physics, and engineering, as well as a research reference for professionals in those fields." (Lokenath Debnath, SIAM Review, Vol. 53 (1), 2011)"This is an introductory and elementary textbook about Sato's hyperfunctions in one variable and some of their integral transforms. . mainly addressed to applied mathematicians, physicists and engineers, it may also be useful for pure mathematicians seeking a first encounter with Sato's beautiful conception of generalized functions. . The only prerequisites for the reader are elementary notions from complex function theory of one variable and some familiarity with the classical Laplace transform. This makes the material of the book accessible even to undergraduate students." (Jasson Vindas, Mathematical Reviews, Issue 2012 a)"This monograph aims at introducing the theory of hyperfunctions and some of their integral transforms to a wide range of readers, since the author recognized that the noble idea of hyperfunction was known to only few mathematicians." (Dohan Kim, Zentralblatt MATH, Vol. 1201, 2011)