p-Adic quantum calculus and ideals of compact operators

TL;DR

This paper introduces a quantum differentiation operator on p-adic functions, exploring its properties and showing it maps p-adic Besov spaces into Schatten-von Neumann ideals within compact operators.

Contribution

It constructs a novel quantum differentiation operator for p-adic functions and analyzes its mapping properties into Schatten-von Neumann ideals.

Findings

The operator maps p-adic Besov spaces into Schatten-von Neumann ideals.

Properties of the quantum differentiation operator are thoroughly investigated.

The construction bridges p-adic analysis and operator ideals.

Abstract

The paper proposes a construction of a quantum differentiation operator defined on the spaces of complex-valued functions of $p$-adic argument, and taking values in the algebra of bounded operators on a Hilbert space. The properties of this operator are investigated. In particular, it is proved that the differentiation operator maps $p$-adic Besov spaces into Schatten-von Neumann ideals in the algebra of compact operators.