ENGLISH

Carleman’s Formulas in Complex Analysis: Theory and Applications

By Lev Aizenberg (auth.)

Book information

Publisher
Springer Netherlands
Year
1993
ISBN
978-94-010-4695-4, 978-94-011-1596-4
DOI
10.1007/978-94-011-1596-4
Language
english
Format
PDF
Filesize
9 MB (8984886 bytes)
Series
Mathematics and Its Applications 244
Edition
1
Pages
299\316
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Functions of a Complex Variable; SignalImage and Speech Processing; Applications of Mathe

Description

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).

Similar books