Regular variation /:
This book is a comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x. Such functions are much more than a convenient extension of powers. In many limi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1987.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 27. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is a comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x. Such functions are much more than a convenient extension of powers. In many limit theorems regular variation is intrinsic to the result, and exactly characterises the limit behaviour. The book emphasises such characterisations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather then merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and 'second-order' theorems. They go on to discuss the role of regular variation in Abelian, Tauberian, and Mercerian theorems. These results are then applied in analytic number theory, complex analysis, and probability, with the aim above all of setting the theory in context. A widely scattered literature is thus brought together in a unified approach. With several appendices and a comprehensive list of references, analysts, number theorists, and probabilists will find this an invaluable and complete account of regular variation. It will provide a rigorous and authoritative introduction to the subject for research students in these fields. |
| Beschreibung: | Includes indexes. |
| Beschreibung: | 1 online resource (xix, 491 pages) : illustrations |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references (pages 445-466). |
| ISBN: | 9781107087651 1107087651 9780511721434 0511721439 |
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| 505 | 0 | |a Karamata theory -- Further Karamata theory -- De Haan theory -- Abelian and Tauberian theorems -- Mercerian theorems -- Applications to analytic number theory -- Applications to complex analysis -- Applications to probability theory -- Appendices. | |
| 520 | |a This book is a comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x. Such functions are much more than a convenient extension of powers. In many limit theorems regular variation is intrinsic to the result, and exactly characterises the limit behaviour. The book emphasises such characterisations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather then merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and 'second-order' theorems. They go on to discuss the role of regular variation in Abelian, Tauberian, and Mercerian theorems. These results are then applied in analytic number theory, complex analysis, and probability, with the aim above all of setting the theory in context. A widely scattered literature is thus brought together in a unified approach. With several appendices and a comprehensive list of references, analysts, number theorists, and probabilists will find this an invaluable and complete account of regular variation. It will provide a rigorous and authoritative introduction to the subject for research students in these fields. | ||
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| author | Bingham, N. H. |
| author2 | Goldie, C. M. Teugels, Jef L. |
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| contents | Karamata theory -- Further Karamata theory -- De Haan theory -- Abelian and Tauberian theorems -- Mercerian theorems -- Applications to analytic number theory -- Applications to complex analysis -- Applications to probability theory -- Appendices. |
| ctrlnum | (OCoLC)802299813 |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn802299813 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:24:52Z |
| institution | BVB |
| isbn | 9781107087651 1107087651 9780511721434 0511721439 |
| language | English |
| oclc_num | 802299813 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xix, 491 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Bingham, N. H. Regular variation / N.H. Bingham, C.M. Goldie, J.L. Teugels. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987. 1 online resource (xix, 491 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 27 Includes bibliographical references (pages 445-466). Includes indexes. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2012. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2012 HathiTrust Digital Library committed to preserve pda MiAaHDL Print version record. Karamata theory -- Further Karamata theory -- De Haan theory -- Abelian and Tauberian theorems -- Mercerian theorems -- Applications to analytic number theory -- Applications to complex analysis -- Applications to probability theory -- Appendices. This book is a comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x. Such functions are much more than a convenient extension of powers. In many limit theorems regular variation is intrinsic to the result, and exactly characterises the limit behaviour. The book emphasises such characterisations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather then merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and 'second-order' theorems. They go on to discuss the role of regular variation in Abelian, Tauberian, and Mercerian theorems. These results are then applied in analytic number theory, complex analysis, and probability, with the aim above all of setting the theory in context. A widely scattered literature is thus brought together in a unified approach. With several appendices and a comprehensive list of references, analysts, number theorists, and probabilists will find this an invaluable and complete account of regular variation. It will provide a rigorous and authoritative introduction to the subject for research students in these fields. Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Calculus. http://id.loc.gov/authorities/subjects/sh85018802 Fonctions de variables réelles. Calcul infinitésimal. calculus. aat MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Calculus fast Functions of real variables fast Reguläres Variationsproblem gnd http://d-nb.info/gnd/4401284-6 Fonctions d'une variable réelle. ram Calculus Functions of real variables Goldie, C. M. Teugels, Jef L. Print version: (DLC) 86028422 (OCoLC)14719199 Encyclopedia of mathematics and its applications ; v. 27. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569298 Volltext |
| spellingShingle | Bingham, N. H. Regular variation / Encyclopedia of mathematics and its applications ; Karamata theory -- Further Karamata theory -- De Haan theory -- Abelian and Tauberian theorems -- Mercerian theorems -- Applications to analytic number theory -- Applications to complex analysis -- Applications to probability theory -- Appendices. Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Calculus. http://id.loc.gov/authorities/subjects/sh85018802 Fonctions de variables réelles. Calcul infinitésimal. calculus. aat MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Calculus fast Functions of real variables fast Reguläres Variationsproblem gnd http://d-nb.info/gnd/4401284-6 Fonctions d'une variable réelle. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052357 http://id.loc.gov/authorities/subjects/sh85018802 http://d-nb.info/gnd/4401284-6 |
| title | Regular variation / |
| title_auth | Regular variation / |
| title_exact_search | Regular variation / |
| title_full | Regular variation / N.H. Bingham, C.M. Goldie, J.L. Teugels. |
| title_fullStr | Regular variation / N.H. Bingham, C.M. Goldie, J.L. Teugels. |
| title_full_unstemmed | Regular variation / N.H. Bingham, C.M. Goldie, J.L. Teugels. |
| title_short | Regular variation / |
| title_sort | regular variation |
| topic | Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Calculus. http://id.loc.gov/authorities/subjects/sh85018802 Fonctions de variables réelles. Calcul infinitésimal. calculus. aat MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Calculus fast Functions of real variables fast Reguläres Variationsproblem gnd http://d-nb.info/gnd/4401284-6 Fonctions d'une variable réelle. ram |
| topic_facet | Functions of real variables. Calculus. Fonctions de variables réelles. Calcul infinitésimal. calculus. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Calculus Functions of real variables Reguläres Variationsproblem Fonctions d'une variable réelle. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569298 |
| work_keys_str_mv | AT binghamnh regularvariation AT goldiecm regularvariation AT teugelsjefl regularvariation |