LEADER 05415nam 2200661 a 450 001 9910811156603321 005 20240516114144.0 010 $a981-4366-85-4 035 $a(CKB)2550000000087657 035 $a(EBL)846133 035 $a(SSID)ssj0000734525 035 $a(PQKBManifestationID)11465252 035 $a(PQKBTitleCode)TC0000734525 035 $a(PQKBWorkID)10723851 035 $a(PQKB)10220880 035 $a(MiAaPQ)EBC846133 035 $a(WSP)00008266 035 $a(Au-PeEL)EBL846133 035 $a(CaPaEBR)ebr10529360 035 $a(CaONFJC)MIL498438 035 $a(OCoLC)877768010 035 $a(EXLCZ)992550000000087657 100 $a20120210d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAsympototic behavior of generalized functions$b[electronic resource] /$fSteven Pilipovic?, Bogoljub Stankovic?, Jasson Vindas 205 $a1st ed. 210 $aSingapore $cWorld Scientific$dc2012 215 $a1 online resource (309 p.) 225 1 $aSeries on analysis, applications and computation,$x1793-4702 ;$vv. 5 300 $aDescription based upon print version of record. 311 $a981-4366-84-6 320 $aIncludes bibliographical references (p. 283-292) and index. 327 $aPreface; Contents; I. Asymptotic Behavior of Generalized Functions; 0 Preliminaries; 1 S-asymptotics in F'g; 1.1 Definition; 1.2 Characterization of comparison functions and limits; 1.3 Equivalent definitions of the S-asymptotics in F'; 1.4 Basic properties of the S-asymptotics; 1.5 S-asymptotic behavior of some special classes of generalized functions; 1.5.1 Examples with regular distributions; 1.5.2 Examples with distributions in subspaces of D'; 1.5.3 S-asymptotics of ultradistributions and Fourier hyperfunctions - Comparisons with the S-asymptotics of distributions 327 $a1.6 S-asymptotics and the asymptotics of a function1.7 Characterization of the support of T F'; 1.8 Characterization of some generalized function spaces; 1.9 Structural theorems for S-asymptotics in F'; 1.10 S-asymptotic expansions in F'g; 1.10.1 General definitions and assertions; 1.10.2 S-asymptotic Taylor expansion; 1.11 S-asymptotics in subspaces of distributions; 1.12 Generalized S-asymptotics; 2 Quasi-asymptotics in F'; 2.1 Definition of quasi-asymptotics at infinity over a cone; 2.2 Basic properties of quasi-asymptotics over a cone 327 $a2.3 Quasi-asymptotic behavior at infinity of some generalized functions2.4 Equivalent definitions of quasi-asymptotics at infinity; 2.5 Quasi-asymptotics as an extension of the classical asymptotics; 2.6 Relations between quasi-asymptotics in D'(R) and S'(R); 2.7 Quasi-asymptotics at ±; 2.8 Quasi-asymptotics at the origin; 2.9 Quasi-asymptotic expansions; 2.10 The structure of quasi-asymptotics. Up-to-date results in one dimension; 2.10.1 Remarks on slowly varying functions; 2.10.2 Asymptotically homogeneous functions 327 $a2.10.3 Relation between asymptotically homogeneous functions and quasi-asymptotics2.10.4 Associate asymptotically homogeneous functions; 2.10.5 Structural theorems for negative integral degrees. The general case; 2.11 Quasi-asymptotic extension; 2.11.1 Quasi-asymptotics at the origin in D'(R) and S'(R); 2.11.2 Quasi-asymptotic extension problem in D'(0, ); 2.11.3 Quasi-asymptotics at infinity and spaces V'ß (R); 2.12 Quasi-asymptotic boundedness; 2.13 Relation between the S-asymptotics and quasi-asymptotics at; II. Applications of the Asymptotic Behavior of Generalized Functions 327 $a3 Asymptotic behavior of solutions to partial differential equations3.1 S-asymptotics of solutions; 3.2 Quasi-asymptotics of solutions; 3.3 S-asymptotics of solutions to equations with ultra-differential or local operators; 4 Asymptotics and integral transforms; 4.1 Abelian type theorems; 4.1.1 Transforms with general kernels; 4.1.2 Special integral transforms; 4.2 Tauberian type theorems; 4.2.1 Convolution type transforms in spaces of distributions; 4.2.2 Convolution type transforms in other spaces of generalized functions; 4.2.3 Integral transforms of Mellin convolution type 327 $a4.2.4 Special integral transforms 330 $aThe asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach - of Estrada, Kanwal and Vindas - is related 410 0$aSeries on analysis, applications and computation ;$vv. 5. 606 $aAsymptotic expansions 615 0$aAsymptotic expansions. 676 $a515.23 676 $a515.782 700 $aPilipovic?$b Stevan$01713645 701 $aStankovic?$b Bogoljub$f1924-$01713646 701 $aVindas$b Jasson$01101708 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811156603321 996 $aAsympototic behavior of generalized functions$94106781 997 $aUNINA