Decompositions of Gelfand-Shilov kernels into kernels of similar class

TL;DR

This paper demonstrates that operators with Gelfand-Shilov kernels can be decomposed into compositions of similar kernels, providing insights into their structure and implications for numerical approximation and Schatten-von Neumann properties.

Contribution

It introduces a novel decomposition method for Gelfand-Shilov kernels and explores their applications in operator theory and numerical analysis.

Findings

Operators with Gelfand-Shilov kernels can be decomposed into two similar kernels.

Established links between these decompositions and numerical approximation techniques.

Proved Schatten-von Neumann properties for such operators.

Abstract

We prove that any linear operator with kernel in a Gelfand-Shilov space is a composition of two operators with kernels in the same Gelfand-Shilov space. We also give links on numerical approximations for such compositions. We apply these composition rules to establish Schatten-von Neumann properties for such operators.