Asympototic behavior of generalized functions [[electronic resource] /] / Steven Pilipović, Bogoljub Stanković, Jasson Vindas |
Autore | Pilipović Stevan |
Pubbl/distr/stampa | Singapore, : World Scientific, c2012 |
Descrizione fisica | 1 online resource (309 p.) |
Disciplina |
515.23
515.782 |
Altri autori (Persone) |
StankovićBogoljub <1924->
VindasJasson |
Collana | Series on analysis, applications and computation |
Soggetto topico | Asymptotic expansions |
Soggetto genere / forma | Electronic books. |
ISBN | 981-4366-85-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Preface; 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
1.6 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 2.3 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 2.10.3 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 3 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 4.2.4 Special integral transforms |
Record Nr. | UNINA-9910457493803321 |
Pilipović Stevan
![]() |
||
Singapore, : World Scientific, c2012 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Asympototic behavior of generalized functions [[electronic resource] /] / Steven Pilipović, Bogoljub Stanković, Jasson Vindas |
Autore | Pilipović Stevan |
Pubbl/distr/stampa | Singapore, : World Scientific, c2012 |
Descrizione fisica | 1 online resource (309 p.) |
Disciplina |
515.23
515.782 |
Altri autori (Persone) |
StankovićBogoljub <1924->
VindasJasson |
Collana | Series on analysis, applications and computation |
Soggetto topico | Asymptotic expansions |
ISBN | 981-4366-85-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Preface; 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
1.6 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 2.3 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 2.10.3 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 3 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 4.2.4 Special integral transforms |
Record Nr. | UNINA-9910779068103321 |
Pilipović Stevan
![]() |
||
Singapore, : World Scientific, c2012 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Asympototic behavior of generalized functions [[electronic resource] /] / Steven Pilipović, Bogoljub Stanković, Jasson Vindas |
Autore | Pilipović Stevan |
Edizione | [1st ed.] |
Pubbl/distr/stampa | Singapore, : World Scientific, c2012 |
Descrizione fisica | 1 online resource (309 p.) |
Disciplina |
515.23
515.782 |
Altri autori (Persone) |
StankovićBogoljub <1924->
VindasJasson |
Collana | Series on analysis, applications and computation |
Soggetto topico | Asymptotic expansions |
ISBN | 981-4366-85-4 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Preface; 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
1.6 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 2.3 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 2.10.3 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 3 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 4.2.4 Special integral transforms |
Record Nr. | UNINA-9910811156603321 |
Pilipović Stevan
![]() |
||
Singapore, : World Scientific, c2012 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|