Complex Analysis and Potential TheoryAndre Boivin, Javad Mashreghi American Mathematical Soc., 2012 - 329 pàgines 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 Mathematiques (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. |
Continguts
A Simple Numerical Approach to the Riemann Hypothesis | 21 |
A Unifying Construction for MeasureValued Continuous and Discrete | 47 |
Compactifications of the Plane and Extensions of the Disc Algebra | 61 |
Examples of Quantitative Universal Approximation | 77 |
Harmonic Mappings with Quadrilateral Image | 99 |
Hartogs Phenomenon on Unbounded DomainsConjectures and Examples | 117 |
Integration Formulae and Kernels in Singular Subvarieties of | 135 |
Invariant Potential Theory Derivatives of Inner Functions and Bpq Spaces | 149 |
On a Family of Outer Functions | 193 |
On CmSubharmonic Extension Sets of WalshType | 201 |
On Universality of Series in Banach Spaces | 217 |
Potential Analysis on Nonsmooth DomainsMartin Boundary and Boundary | 235 |
Potential Theory on Trees and Multiplication Operators | 255 |
Recent Progress on Fine Differentiability and Fine Harmonicity | 283 |
Subordinate Harmonic Structures in an Infinite Network | 301 |
The Generalized Binomial Theorem | 315 |
Frases i termes més freqüents
algebra Amer approximation arcs assume ball Banach Bergman spaces biharmonic boundary Harnack principle bounded Brelot space Brelot structure compact set compact subset compactification complex condition connected consider constant contains continuous function converges Corollary CR function defined Definition denote differential Dirichlet disk E-mail address equation Euclidean example exists finite first fixed formula function f given Green function Hardy space harmonic function Hence holomorphic function inequality inner function integral Jordan arc kernel Lemma Let f linear Lipschitz domain mapping Martin boundary Math measure meromorphic metric neighborhood nonnegative open set P-harmonic P-potential polynomials positive harmonic function potential theory prove respect result Riemann surface Riesz satisfies satisfying Section sequence solution Springer subharmonic superharmonic functions Theorem 2.1 topology tree uniform domain uniformly unique unit disc univalent universal Taylor series vertex vertices zero