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• W2097234227 abstract "Complex-analytic and related boundary properties of transforms give information on the behavior of pre-images. The transforms may be power series, Dirichlet series or Laplace-type integrals; the pre-images are series (of numbers) or functions. The chief impulse for complex Tauberian theory came from number theory. The first part of the survey emphasizes methods which permit simple derivations of the prime number theorem, associated with the labels Landau-Wiener-Ikehara and Newman. Other important areas in complex Tauberian theory are associated with the names Fatou-Riesz and Ingham. Recent refinements have been motivated by operator theory and include local<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Superscript 1><mml:semantics><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:annotation encoding=application/x-tex>H^1</mml:annotation></mml:semantics></mml:math></inline-formula>and pseudofunction boundary behavior of transforms. Complex information has also led to better remainder estimates in connection with classical Tauberian theorems. Applications include the distribution of zeros and eigenvalues." @default.
• W2097234227 created "2016-06-24" @default.
• W2097234227 creator A5036049909 @default.
• W2097234227 date "2002-07-08" @default.
• W2097234227 modified "2023-09-27" @default.
• W2097234227 title "A century of complex Tauberian theory" @default.
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• W2097234227 doi "https://doi.org/10.1090/s0273-0979-02-00951-5" @default.
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