On sequences preserving summability

TL;DR

This paper investigates sequences of positive numbers that preserve summability, exploring their properties and introducing various classes such as polynomials, power sums, and solutions to difference equations.

Contribution

It characterizes the open set property for sequences preserving summability and introduces new classes of such sequences, expanding understanding of their structure.

Findings

Identified the open set property for sequences preserving summability

Introduced classes including polynomials and power sums that preserve summability

Analyzed solutions of certain difference equations as summability-preserving sequences

Abstract

In this paper, we study sequences of positive numbers preserving summability. In particular, the open set property for such a family of sequences is shown. Several classes of sequences preserving summability, including polynomials, sums of powers, and solutions of some difference equations, are introduced.