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

Aizenberg, L.A.

ISBN 10: 9401046956 / ISBN 13: 9789401046954

Edité par Springer, 2012

A propos de cet article

N° de réf. du vendeur I-9789401046954

Détails bibliographiques

• Titre: Carleman?s Formulas in Complex Analysis: Theory and Applications (Mathematics and Its Applications)
• Éditeur: Springer
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 9401046956
• ISBN à 13 chiffres: 9789401046954
• Reliure: Couverture souple
• État de l'article: New

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.