相关论文: The concentration index of subharmonic functions o…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
The definition of order indices for density matrices is extended to finite systems. This makes it possible to characterize the level of ordering in such finite systems as macromolecules, nanoclusters, quantum dots, or trapped atoms. The…
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
It is known that a subharmonic function of finite order $\rho$ can be approximated by the logarithm of the modulus of an entire function at the point $z$ outside an exceptional set up to $C\log|z|$. In this article we prove that if such an…
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions becomes an entire function. Moreover, as an example of such functions, we study a function called Poincare…
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
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.
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of 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…
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
In this paper, we define a subclass of sense-preserving harmonic functions associated with a class of analytic functions satisfying a differential inequality. We then establish a close relation between both subclasses. Further, we obtain…
In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…
We investigate {\bf explicit} universal estimate of finite Morse index solutions to polyharmonic equations. \,Differently to previous works \cite{BL2, DDF, fa, H1}, propose here a direct proof using a new interpolation inequality and a…
An extension of sinc interpolation on $\mathbb{R}$ to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces…
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
We study semifinite harmonic functions on arbitrary branching graphs. We give a detailed exposition of an algebraic method which allows one to classify semifinite indecomposable harmonic functions on some multiplicative branching graphs.…