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＜電子ブック＞
Tauberian Theory : A Century of Developments / by Jacob Korevaar
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 329)

版	1st ed. 2004.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	XV, 483 p : online resource
著者標目	*Korevaar, Jacob author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Sequences (Mathematics) LCSH:Approximation theory LCSH:Fourier analysis LCSH:Number theory FREE:Analysis FREE:Sequences, Series, Summability FREE:Approximations and Expansions FREE:Fourier Analysis FREE:Integral Transforms and Operational Calculus FREE:Number Theory
一般注記	I The Hardy—Littlewood Theorems -- II Wiener’s Theory -- III Complex Tauberian Theorems -- IV Karamata’s Heritage: Regular Variation -- V Extensions of the Classical Theory -- VI Borel Summability and General Circle Methods -- VII Tauberian Remainder Theory -- References 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 HTTP:URL=https://doi.org/10.1007/978-3-662-10225-1

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