Univalent Harmonic Mappings of Annuli
Universal Taylor series, conformal mappings and boundary behaviour
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Use of logarithmic sums to estimate polynomials.
Voiculescu’s Entropy and Potential Theory
We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.
Weighted polynomial approximation in the complex plane.
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
Wiener's type regularity criteria on the complex plane
We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is Hölder continuous....
Zero distributions via orthogonality
We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We illustrate the procedure in four cases: classical orthogonality, non-Hermitian orthogonality, orthogonality in rational approximation of Markov functions and its non- Hermitian variant.
Zero sets of functions in harmonic Hardy spaces.
Zeros of Sequences of Partial Sums and Overconvergence
2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated....
Zur Holomorphie des Poissonintegrals.
Zur Integration der Differentialgleichung ... = 0.
Аналог теоремы Валирона-Титчмарша для двучленных асимптотик субгармонической функции с массами на конечной системе лучей.
Аномалии Вуда в задаче дифракции плоской волны на гладкой периодической границе
Аппроксимация однородных субгармонических функций
Асимптотика коэффициентов возбуждения плоских волн в задаче с волнистой периодической границей
Асимтотическая аппроксимация субгармонических функций.
Биголоморфность решений обратной краевой задачи в
Граничное искажение и измерение модуля при расширении двусвязной области
Дифференцируемость решений некоторых задач теории потенциала