Tsallis' q-analysis, new scales of interpolating spaces and q-rational functions

TL;DR

This paper develops a quantum calculus framework based on Tsallis' q-exponential, introducing new scales of interpolating spaces and q-rational functions to enhance mathematical tools for quantum analysis.

Contribution

It introduces new scales of interpolating spaces and q-rational functions within Tsallis' q-analysis, expanding the mathematical toolkit for quantum calculus.

Findings

Development of q-Fock spaces and structural identities

Introduction of new q-interpolating spaces

Formulation of q-rational functions in quantum calculus

Abstract

We are studying the fundamental tools for a quantum calculus based on the Tsallis $q$-exponential In particular we are looking at $q$-Fock spaces, structural identities, as well as rational functions in this context.