Related papers: Radial limits and boundary uniqueness
The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.
We prove the universality of the regular realizability problems for several classes of filters. The filters are encodings of finite relations on the set of non-negative integers in the format proposed by P. Wolf and H. Fernau. The…
The paper generalizes Lazarus Fuchs' theorem on the solutions of complex ordinary linear differential equations with regular singularities to the case of ground fields of arbitrary characteristic, giving a precise description of the shape…
Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin's recursion formula for describing the radial parts of fundamental operators in general linear and ortho-symplectic cases is…
19th century real analysis received a major impetus from Cauchy's work. Cauchy mentions variable quantities, limits, and infinitesimals, but the meaning he attached to these terms is not identical to their modern meaning. Some Cauchy…
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…
In this paper, we develop Pesin theory for the boundary map of some Fatou components of transcendental functions, under certain hyptothesis on the singular values and the Lyapunov exponent. That is, we prove that generic inverse branches…
We discuss how the finiteness and universality of the speed of light arise in the theoretical framework introduced in [1], and derive generalized coordinate transformations, that allow to investigate physical systems in a non-classical…
In this paper we study two notions of differentiability introduced by P. Cannarsa and G. Da Prato (see [28]) and L. Gross (see [56]) in both the framework of infinite dimensional analysis and the framework of Malliavin calculus.
In this paper, we present a slightly modified version of Fra\"iss\'e theory which is used in a paper by Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, Vladyslav Kalashnyk and Martino Lupini (arXiv:1411.4066) and another by…
In this paper we prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the $p$-Laplacian operator with Dirichlet boundary conditions on a bounded domain having nontrivial topology…
This is a survey paper that discusses the original bounds of the seminal papers by Chernoff and Hoeffding. Moreover, it includes a variety of derivative bounds in a variety of forms. Complete proofs are provided as needed. The intent is to…
We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…
We consider the question whether a Sylow like theorem is valid in the normalized units of integral group rings of finite groups. After a short survey on the known results we show that this is the case for integral group rings of Frobenius…
We analyze the boundaries of multiply connected Fatou components of transcendental maps by means of universal covering maps and associated inner functions. A unified approach is presented, which includes invariant Fatou components (of any…
The study of the structure of infinite words having bounded abelian complexity was initiated by G. Richomme, K. Saari, and L. Q. Zamboni. In this note we define bounded additive complexity for infinite words over a finite subset of Z^m. We…
We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…
The paper provides the proof of the Rimann's conjecture. The results of the works of A. M. Odlyzko and H. te Riile "Disproof of the Conjecture", which gives a disproof of the Mertens hypothesis, using to prove the Riemann's hypothesis. This…
We give a combinatorial extension of the classical inequalities of Maclaurin about symmetric functions of several variables. We discuss two problems - one analytical and another combinatorial - and show that they are in some sense…
A novel way of defining limits in classical statistics is proposed. This is a natural extension of the original Neyman's method, and has the desirable property that only information relevant to the problem is used in making statistical…