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carleman s formulas in complex analysis: theory and applications (in English)
L. a. Aizenberg
(Author)
·
Springer
· Hardcover
carleman s formulas in complex analysis: theory and applications (in English) - Aizenberg, L. a.
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Synopsis "carleman s formulas in complex analysis: theory and applications (in English)"
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).
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The book is written in English.
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