Carleman's Formulas in Complex Analysis: Theory and Applications

By Lev Abramovich Aizenberg

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).

• Format: Hardcover
• Language: English
• ISBN: 0792321219
• ISBN13: 9780792321217
• Release Date: January 1993
• Publisher: Springer
• Length: 299 Pages
• Weight: 1.44 lbs.
• Dimensions: 0.9" x 6.5" x 9.6"