Carleman’s Formulas in Complex Analysis: Theory and Applications (Mathematics and Its Applications, 244)

Aizenberg, L.A.

ISBN 10: 0792321219 / ISBN 13: 9780792321217

Published by Springer, 1993

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Bibliographic Details

• Title: Carleman?s Formulas in Complex Analysis: Theory and Applications (Mathematics and Its Applications, 244)
• Publisher: Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 0792321219
• ISBN 13: 9780792321217
• Binding: Hardcover
• Condition: New

About this title

Synopsis

Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com­ plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)). They solve the classical problem of recovering at the points of a do­ main D a holomorphic function that is sufficiently well-behaved when approaching the boundary aD, from its values on aD or on S. Alongside with this classical problem, it is possible and natural to consider the following one: to recover the holomorphic function in D from its values on some set MeaD not containing S. Of course, M is to be a set of uniqueness for the class of holomorphic functions under consideration (for example, for the functions continuous in D or belonging to the Hardy class HP(D), p ~ 1).

Synopsis

This monograph gives a systematic presentation of the Carleman formulas. These enable values of functions holomorphic to a domain to be recovered from their values over a part of the boundary of the domain. Various generalizations of these formulas are considered. Applications are considered to problems of analytic continuation in the theory of functions, and, in a broader context, to problems arising in theoretical and mathematical physics, and to the extrapolation and interpolation of signals having a finite Fourier spectrum. The volume also contains a review of recent results, including those obtained by computer simulation on the elimination of noise in a given frequency band. It is suitable for mathematicians and theoretical physicists whose work involves complex analysis, and those interested in signal processing.