Convolution type integral equations in the conservative case

TL;DR

This paper investigates convolution type integral equations in the conservative case, where classical Fourier methods face difficulties, and introduces a special factorization method to analyze these equations.

Contribution

It presents a novel factorization approach tailored for convolution equations in the conservative case, addressing limitations of traditional Fourier techniques.

Findings

Developed a new factorization method for conservative convolution equations

Provided analytical tools for equations with degenerate symbols

Enhanced understanding of non-normal convolution equations

Abstract

In this paper convolution type integral equations in the conservative case are studied. The conservative case of convolution type of equations relates to the case of non normal type of equations and is that of the corresponding symbols degenerate at some points of the real line, and the classical Furier transformation method meets difficulties with its application to the studying equations. To the study in the conservative case of convolution type equations in this paper we use the special factorization method.