Asymptotic behavior of generalized functions /:
The 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...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore :
World Scientific,
©2012.
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| Schriftenreihe: | Series on analysis, applications and computation ;
v. 5. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The 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. |
| Beschreibung: | 1 online resource (xiii, 294 pages) |
| Bibliographie: | Includes bibliographical references (pages 283-292) and index. |
| ISBN: | 9789814366854 9814366854 |
| ISSN: | 1793-4702 ; |
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| 245 | 1 | 0 | |a Asymptotic behavior of generalized functions / |c Steven Pilipović, Bogoljub Stanković, Jasson Vindas. |
| 260 | |a Singapore : |b World Scientific, |c ©2012. | ||
| 300 | |a 1 online resource (xiii, 294 pages) | ||
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| 490 | 1 | |a Series on analysis, applications and computation, |x 1793-4702 ; |v v. 5 | |
| 504 | |a Includes bibliographical references (pages 283-292) and index. | ||
| 505 | 0 | |6 880-01 |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a The 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. | ||
| 650 | 0 | |a Asymptotic expansions. |0 http://id.loc.gov/authorities/subjects/sh85009056 | |
| 650 | 4 | |a Asymptotic expansions. | |
| 650 | 4 | |a Theory of distributions (Functional analysis) | |
| 650 | 6 | |a Développements asymptotiques. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Asymptotic expansions |2 fast | |
| 700 | 1 | |a Stanković, Bogoljub, |d 1924- |1 https://id.oclc.org/worldcat/entity/E39PBJwX9YPKrvgfpJxmFCCPcP |0 http://id.loc.gov/authorities/names/n84075589 | |
| 700 | 1 | |a Vindas, Jasson. | |
| 776 | 0 | 8 | |i Print version: |a Pilipović, Stevan. |t Asympototic behavior of generalized functions. |d Singapore : World Scientific, ©2012 |w (DLC) 2012359710 |
| 830 | 0 | |a Series on analysis, applications and computation ; |v v. 5. |x 1793-4702 |0 http://id.loc.gov/authorities/names/no2007153869 | |
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| 880 | 0 | |6 505-01/(S |a Machine generated contents note: 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 -- 1.6.S-asymptotics and the asymptotics of a function -- 1.7. Characterization of the support of T ε F'o -- 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 -- 1.11.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 functions. | |
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| contents | 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. |
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Up-to-date results in one dimension; 2.10.1 Remarks on slowly varying functions; 2.10.2 Asymptotically homogeneous functions.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The 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. 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| id | ZDB-4-EBA-ocn785777959 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:20Z |
| institution | BVB |
| isbn | 9789814366854 9814366854 |
| issn | 1793-4702 ; |
| language | English |
| oclc_num | 785777959 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 294 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on analysis, applications and computation ; |
| series2 | Series on analysis, applications and computation, |
| spelling | Pilipović, Stevan. Asymptotic behavior of generalized functions / Steven Pilipović, Bogoljub Stanković, Jasson Vindas. Singapore : World Scientific, ©2012. 1 online resource (xiii, 294 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Series on analysis, applications and computation, 1793-4702 ; v. 5 Includes bibliographical references (pages 283-292) and index. 880-01 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. The 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. Asymptotic expansions. http://id.loc.gov/authorities/subjects/sh85009056 Asymptotic expansions. Theory of distributions (Functional analysis) Développements asymptotiques. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Asymptotic expansions fast Stanković, Bogoljub, 1924- https://id.oclc.org/worldcat/entity/E39PBJwX9YPKrvgfpJxmFCCPcP http://id.loc.gov/authorities/names/n84075589 Vindas, Jasson. Print version: Pilipović, Stevan. Asympototic behavior of generalized functions. Singapore : World Scientific, ©2012 (DLC) 2012359710 Series on analysis, applications and computation ; v. 5. 1793-4702 http://id.loc.gov/authorities/names/no2007153869 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521271 Volltext 505-01/(S Machine generated contents note: 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 -- 1.6.S-asymptotics and the asymptotics of a function -- 1.7. Characterization of the support of T ε F'o -- 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 -- 1.11.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 functions. |
| spellingShingle | Pilipović, Stevan Asymptotic behavior of generalized functions / Series on analysis, applications and computation ; 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. Asymptotic expansions. http://id.loc.gov/authorities/subjects/sh85009056 Asymptotic expansions. Theory of distributions (Functional analysis) Développements asymptotiques. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Asymptotic expansions fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85009056 |
| title | Asymptotic behavior of generalized functions / |
| title_auth | Asymptotic behavior of generalized functions / |
| title_exact_search | Asymptotic behavior of generalized functions / |
| title_full | Asymptotic behavior of generalized functions / Steven Pilipović, Bogoljub Stanković, Jasson Vindas. |
| title_fullStr | Asymptotic behavior of generalized functions / Steven Pilipović, Bogoljub Stanković, Jasson Vindas. |
| title_full_unstemmed | Asymptotic behavior of generalized functions / Steven Pilipović, Bogoljub Stanković, Jasson Vindas. |
| title_short | Asymptotic behavior of generalized functions / |
| title_sort | asymptotic behavior of generalized functions |
| topic | Asymptotic expansions. http://id.loc.gov/authorities/subjects/sh85009056 Asymptotic expansions. Theory of distributions (Functional analysis) Développements asymptotiques. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Asymptotic expansions fast |
| topic_facet | Asymptotic expansions. Theory of distributions (Functional analysis) Développements asymptotiques. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Asymptotic expansions |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521271 |
| work_keys_str_mv | AT pilipovicstevan asymptoticbehaviorofgeneralizedfunctions AT stankovicbogoljub asymptoticbehaviorofgeneralizedfunctions AT vindasjasson asymptoticbehaviorofgeneralizedfunctions |