03527nam 2200745 a 450 991078908910332120230803033550.03-11-029851-110.1515/9783110298512(CKB)3390000000032633(EBL)1113319(SSID)ssj0000916760(PQKBManifestationID)11471070(PQKBTitleCode)TC0000916760(PQKBWorkID)10878113(PQKB)10608175(MiAaPQ)EBC1113319(DE-B1597)179026(OCoLC)851970512(OCoLC)853258376(DE-B1597)9783110298512(Au-PeEL)EBL1113319(CaPaEBR)ebr10728955(CaONFJC)MIL503372(EXLCZ)99339000000003263320130624d2013 uy 0engurcn#nnn|||||txtrdacontentcrdamediacrrdacarrierDistribution theory[electronic resource] convolution, Fourier transform, and Laplace transform /Gerrit van DijkBerlin De Gruyter20131 online resource (viii, 105 pages) illustrationsDe Gruyter TextbookDe Gruyter graduate lecturesDescription based upon print version of record.3-11-029591-1 Includes bibliographical references and index.Front matter --Preface --Contents --1 Introduction --2 Definition and First Properties of Distributions --3 Differentiating Distributions --4 Multiplication and Convergence of Distributions --5 Distributions with Compact Support --6 Convolution of Distributions --7 The Fourier Transform --8 The Laplace Transform --9 Summable Distributions --10 Appendix --11 Hints to the Exercises --References --Index --BackmatterThe theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added.De Gruyter graduate lectures.Theory of distributions (Functional analysis)Convolutions (Mathematics)Fourier transformationsLaplace transformationDistribution Theory.Fourier Transform.Heat Equation.Laplace Transform.Tempered Distribution.Theory of distributions (Functional analysis)Convolutions (Mathematics)Fourier transformations.Laplace transformation.515.782SK 600rvkDijk Gerrit van1939-1465854MiAaPQMiAaPQMiAaPQBOOK9910789089103321Distribution theory3676101UNINA