Overview

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).

Full Product Details

Author:   L.A. Aizenberg
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1993
Volume:   244
Dimensions:   Width: 16.00cm , Height: 1.70cm , Length: 24.00cm
Weight:   0.514kg
ISBN:  

9789401046954

ISBN 10:   9401046956
Pages:   299
Publication Date:   29 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

I. Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalizations.- I. One-Dimensional Carleman Formulas.- II. Generalization of One-Dimensional Carleman Formulas.- II. Carleman Formulas in Multidimensional Complex Analysis.- III. Integral Representations of Holomorphic Functions of Several Complex Variables and Logarithmic Residues.- IV. Multidimensional Analog of Carleman Formulas with Integration over Boundary Sets of Maximal Dimension.- V. Multidimensional Carleman Formulas for Sets of Smaller Dimension.- VI. Carleman Formulas in Homogeneous Domains.- III. First Applications.- VII. Applications in Complex Analysis.- VIII. Applications in Physics and Signal Processing.- IX. Computing Experiment.- IV. Supplement to the English Edition.- X. Criteria for Analytic Continuation. Harmonic Extension.- XI. Carleman Formulas and Related Problems.- Notes.- Index of Proper Names.- Index of Symbols.

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