Related papers: On Non-Linear Markov Operators: surjectivity vs or…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous…

We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are…

This paper is devoted to introduce the non linear reconstruction operator PPH on non uniform grids. We define this operator and we study its main properties such as reproduction of polynomials of second degree, approximation order and…

In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis,…

This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.

Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…

Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…

We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say $m$ is a polynomial of degree at most $m\;\text{.}\;$ We show that then under some…

We study non-linear Schr\"odinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear…

In the present article we define the Jain type modification of the generalized Szasz-Mirakjan operators that preserve constant and exponential mappings. Moments, recurrence formulas, and other identities are established for these operators.…

We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew-Hermitian differentiation matrix. While a theory of such L2-orthogonal systems is…

Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…

This semi-expository paper surveys results concerning three classes of orthogonal polynomials: in one non-hermitian variable, in several isometric non-commuting variables, and in several hermitian non-commuting variables. The emphasis is on…

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and…

Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…

We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials

Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…