Title: Carleman?s Formulas in Complex Analysis: Theory and Applications (Mathematics and Its Applications)
Publisher: Springer
Publication Date: 2012
Language: English
ISBN 10: 9401046956
ISBN 13: 9789401046954
Binding: Soft cover
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).

Language Notes

Text: English
Original Language: Russian

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