Related papers: Uniqueness property for quasiharmonic functions

In this paper, we introduce several various classes of $c$-almost periodic type functions and their Stepanov generalizations, where $c\in {\mathbb C}$ and $|c|=1.$ We also consider the corresponding classes of $c$-almost periodic type…

We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…

We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…

In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.

Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the c-differential uniformity of power functions over finite fields. Based on some known almost…

We propose a necessary and sufficient condition for a real-valued function on the real line to be a characteristic function of a probability measures. The statement is given in terms of harmonic functions and completely monotonic functions.

This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.

In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.

In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine…

Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…

In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can conclude that two subharmonic functions which agree almost…

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.

We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…

This article provides a definition of a subdifferential for continuous functions based on homological considerations. We show that it satisfies all the requirement for a good notion of subdifferential. Moreover, we prove sublinearity, a…

We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…

Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures…

In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.

For a continuous function, we prove that the function is pluriharmonic if and only if the equality part of the optimal Ohsawa--Takegoshi $L^2$-extension theorem is satisfied with respect to the metric having the function as a weight. This…