**CRM Proceedings & Lecture Notes**

Volume: 55;
2012;
329 pp;
Softcover

MSC: Primary 30; 31; 32;

Print ISBN: 978-0-8218-9173-5

Product Code: CRMP/55

List Price: $135.00

Individual Member Price: $108.00

**Electronic ISBN: 978-1-4704-1589-1
Product Code: CRMP/55.E**

List Price: $135.00

Individual Member Price: $108.00

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# Complex Analysis and Potential Theory

Share this page *Edited by *
*André Boivin; Javad Mashreghi*

A co-publication of the AMS and Centre de Recherches Mathématiques

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.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## Complex Analysis and Potential Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- A self-contained proof of the strong-type capacitary inequality for the Dirichlet space 114
- A simple numerical approach to the Riemann hypothesis 2134
- A survey of linear extremal problems in analytic function spaces 3346
- A unifying construction for measure-valued continuous and discrete branching processes 4760
- Compactifications of the plane and extensions of the disc algebra 6174
- Examples of quantitative universal approximation 7790
- Harmonic mappings with quadrilateral image 99112
- Hartogs phenomenon on unbounded domains—Conjectures and examples 117130
- Integration formulae and kernels in singular subvarieties of ℂⁿ 135148
- Invariant potential theory, derivatives of inner functions, and 𝐵^{𝑝,𝑞} spaces in the unit ball of ℂⁿ 149162
- Logarithmic Hölder estimates of 𝑝-harmonic extension operators in a metric measure space 163176
- Meromorphic approximation on noncompact Riemann surfaces 171184
- On a family of outer functions 193206
- On 𝐶^{𝑚}-subharmonic extension sets of Walsh-type 201214
- On maximal plurisubharmonic functions 211224
- On universality of series in Banach spaces 217230
- Orlicz capacity of balls 225238
- Potential analysis on nonsmooth domains—Martin boundary and boundary Harnack principle 235248
- Potential theory on trees and mutliplication operators 255268
- Recent progress on fine differentiability and fine harmonicity 283296
- Reversibility questions in groups arising in analysis 293306
- Subordinate harmonic structures in an infinite network 301314
- The generalized binomial theorem 315328
- Uniform and 𝐶^{𝑚}-approximation by polyanalytic polynomials 323336
- Back Cover Back Cover1346

#### Readership

Graduate students and research mathematicians interested in complex analysis and potential theory.