Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovi\'c kernels

TL;DR

This paper establishes factorization, singular value estimates, and Schatten-von Neumann properties for operators with kernels in Gelfand-Shilov and Pilipovi spaces, linking theoretical analysis with numerical approximation methods.

Contribution

It introduces a novel factorization approach for operators with Gelfand-Shilov and Pilipovi kernels and derives new singular value estimates and Schatten class properties.

Findings

Operators can be factorized within the same function space class.

Derived bounds for singular values of these operators.

Established Schatten-von Neumann class membership criteria.

Abstract

We prove that any linear operator with kernel in a Pilipovi\'c or Gelfand-Shilov space can be factorized by two operators in the same class. We also give links on numerical approximations for such compositions. We apply these composition rules to deduce estimates of singular values and establish Schatten-von Neumann properties for such operators.