Tauberian Theory: A Century of Developments
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
329 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book |
| Physical Description: | 1 Online-Ressource (XV, 483 p) |
| ISBN: | 9783662102251 9783642059193 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-10225-1 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662102251 9783642059193 |
| issn | 0072-7830 |
| language | English |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Korevaar, Jacob Verfasser aut Tauberian Theory A Century of Developments by Jacob Korevaar Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XV, 483 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 329 0072-7830 Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Number theory Sequences, Series, Summability Approximations and Expansions Fourier Analysis Integral Transforms, Operational Calculus Number Theory Mathematik Tauber-Sätze (DE-588)4319823-5 gnd rswk-swf Tauber-Sätze (DE-588)4319823-5 s 1\p DE-604 https://doi.org/10.1007/978-3-662-10225-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Korevaar, Jacob Tauberian Theory A Century of Developments Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Number theory Sequences, Series, Summability Approximations and Expansions Fourier Analysis Integral Transforms, Operational Calculus Number Theory Mathematik Tauber-Sätze (DE-588)4319823-5 gnd |
| subject_GND | (DE-588)4319823-5 |
| title | Tauberian Theory A Century of Developments |
| title_auth | Tauberian Theory A Century of Developments |
| title_exact_search | Tauberian Theory A Century of Developments |
| title_full | Tauberian Theory A Century of Developments by Jacob Korevaar |
| title_fullStr | Tauberian Theory A Century of Developments by Jacob Korevaar |
| title_full_unstemmed | Tauberian Theory A Century of Developments by Jacob Korevaar |
| title_short | Tauberian Theory |
| title_sort | tauberian theory a century of developments |
| title_sub | A Century of Developments |
| topic | Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Number theory Sequences, Series, Summability Approximations and Expansions Fourier Analysis Integral Transforms, Operational Calculus Number Theory Mathematik Tauber-Sätze (DE-588)4319823-5 gnd |
| topic_facet | Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Number theory Sequences, Series, Summability Approximations and Expansions Fourier Analysis Integral Transforms, Operational Calculus Number Theory Mathematik Tauber-Sätze |
| url | https://doi.org/10.1007/978-3-662-10225-1 |
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