Complex Analysis and Potential Theory ( CRM Proceedings & Lecture Notes )

Publication series :CRM Proceedings & Lecture Notes

Author: André Boivin;Javad Mashreghi  

Publisher: American Mathematical Society‎

Publication year: 2012

E-ISBN: 9781470415891

P-ISBN(Paperback): 9780821891735

Subject: O174.5 complex - variable function

Keyword: 暂无分类

Language: ENG

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Complex Analysis and Potential Theory

Description

This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathématiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.

Chapter

Title page

Contents

Preface

A self-contained proof of the strong-type capacitary inequality for the Dirichlet space

A simple numerical approach to the Riemann hypothesis

A survey of linear extremal problems in analytic function spaces

A unifying construction for measure-valued continuous and discrete branching processes

Compactifications of the plane and extensions of the disc algebra

Examples of quantitative universal approximation

Harmonic mappings with quadrilateral image

Hartogs phenomenon on unbounded domains—Conjectures and examples

Integration formulae and kernels in singular subvarieties of ℂⁿ

Invariant potential theory, derivatives of inner functions, and 𝐵^{𝑝,𝑞} spaces in the unit ball of ℂⁿ

Logarithmic Hölder estimates of 𝑝-harmonic extension operators in a metric measure space

Meromorphic approximation on noncompact Riemann surfaces

On a family of outer functions

On 𝐶^{𝑚}-subharmonic extension sets of Walsh-type

On maximal plurisubharmonic functions

On universality of series in Banach spaces

Orlicz capacity of balls

Potential analysis on nonsmooth domains—Martin boundary and boundary Harnack principle

Potential theory on trees and mutliplication operators

Recent progress on fine differentiability and fine harmonicity

Reversibility questions in groups arising in analysis

Subordinate harmonic structures in an infinite network

The generalized binomial theorem

Uniform and 𝐶^{𝑚}-approximation by polyanalytic polynomials

Back Cover

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