# Carleman’s Formulas in Complex Analysis

## Theory and Applications

• Lev Aizenberg
Book

Part of the Mathematics and Its Applications book series (MAIA, volume 244)

1. Front Matter
Pages i-xx
2. ### Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalizations

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Pages 1-17
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Pages 18-32
3. ### Carleman Formulas in Multidimensional Complex Analysis

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Pages 101-128
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Pages 129-142
4. ### First Applications

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Pages 143-162
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Pages 163-191
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Pages 192-203
5. ### Supplement to the English Edition

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Pages 204-251
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Pages 252-275
6. Back Matter
Pages 276-299

### Introduction

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).

### Keywords

Complex analysis Mathematica Symbol signal processing

#### Authors and affiliations

• Lev Aizenberg
• 1
1. 1.Department of Function TheoryInstitute of PhysicsKrasnoyarskSiberia

### Bibliographic information

• DOI https://doi.org/10.1007/978-94-011-1596-4