Selected Topics in Complex Analysis: The S. Ya. Khavinson Memorial Volume

ISBN-13: 9783764372514 / Angielski / Twarda / 2005 / 224 str.

Vladimir Eiderman; Mikhail Samokhin

Opis

This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.

Spis treści

Semyon Yakovlevich Khavinson (May 17, 1927 – January 30, 2003).- S.Ya. Khavinson: Bibliography.- S.Ya. Khavinson: Photos.- The Structural Formulae for Extremal Functions in Hardy Classes on Finite Riemann Surfaces.- Extremal Problems for Nonvanishing Functions in Bergman Spaces.- Generalization of Carathéodory’s Inequality and the Bohr Radius for Multidimensional Power Series.- Remarks on the Value Distribution of Meromorphic Functions.- Approximation Problems on the Unit Sphere in C2.- Conformal Maps and Uniform Approximation by Polyanalytic Functions.- Capacities of Generalized Cantor Sets.- On A?,?P Spaces in the Half-Plane.- Estimate of the Cauchy Integral over Ahlfors Regular Curves.- Quasinormal Families of Meromorphic Functions II.- The Backward Shift on Hp.- On Some Classes of q-parametric Positive linear Operators.

Blurb

This volume is dedicated to the memory of the outstanding mathematician S.Ya. Khavinson. It begins with an expository paper by V.P. Havin presenting a comprehensive survey of Khavinson's works as well as certain biographical material. The complete bibliography following this paper has not previously been published anywhere. It consists of 163 items; a considerable part of these cannot be found in easily accessible sources. The book also contains a series of photographs and twelve original peer-reviewed research and expository papers by leading mathematicians worldwide, including the joint paper by S.Ya. Khavinson and T.S. Kuzina (the last publication of S.Ya. Khavinson).
The main topics covered are extremal problems for various classes of functions, approximation problems, Cauchy integral and analytic capacity,
Cantor sets, meromorphic functions (value distribution, quasinormal families), Carathéodory inequality, integral representation of functions, and the shift operator.
The book is suitable for graduate students and researchers interested in analysis.