Carleman's Formulas in Complex Analysis

L. A. Aizenberg

ISBN 10: 9401046956 / ISBN 13: 9789401046954

Edité par Springer Netherlands, Springer Netherlands Okt 2012, 2012

A propos de cet article

This item is printed on demand - Print on Demand Titel. Neuware -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).Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 320 pp. Englisch.

N° de réf. du vendeur 9789401046954

Détails bibliographiques

• Titre: Carleman's Formulas in Complex Analysis
• Éditeur: Springer Netherlands, Springer Netherlands Okt 2012
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 9401046956
• ISBN à 13 chiffres: 9789401046954
• Reliure: Taschenbuch
• État de l'article: Neu

A propos de ce titre

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).

Présentation de l'éditeur

This monograph is the first to give 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 the latest results, including those obtained by computer simulation on the elimination of noise in a given frequency band. For mathematicians and theoretical physicists whose work involves complex analysis, and those interested in signal processing.