Related papers: A note on rational numbers and certain operators
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and $q$-shift operators can appear. Our summability criteria rely on three ingredients…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
We introduce the notion of $Q$-commuting operators which is a generalization of commuting operators. We prove a generalized version of commutant lifting theorem and Ando's dilation theorem in the context of $Q$-commuting operators.
The article is devoted to the investigation of representation of rational numbers by Cantor series. Necessary and sufficient conditions for a rational number to be representable by a positive Cantor series are formulated for the case of an…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
This survey is devoted to necessary and suffcient conditions for a rational number to be representable by a Cantor series. Necessary and suffcient conditions are formulated for the case of an arbitrary sequence $(q_k)$.
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
The present article is devoted to one class of generalizations of the Salem functions. To construct such functions by systems of functional equations, the generalized shift operator is used.
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
We construct the number operator for particles obeying infinite statistics, defined by a generalized q-deformation of the Heisenberg algebra, and prove the positivity of the norm of linearly independent state vectors.
We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
This paper presents a new formula for the q-shift operator, building on the techniques by Liu and Sears. This formula provides fresh proof of the Carlitz formula and extends it naturally. As applications, we derive an equivalent form of the…
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…
In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introduced and considered.
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
In this article, we determine conditions on the parameters of a generalized convolution operator such that it belongs to the Hardy space and to the space of bounded analytic functions. Results obtained are new and their usefulness is…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…