Krein systems

TL;DR

This paper extends Krein system results to matrix-valued accelerants with discontinuities, providing explicit formulas and leveraging recent advances in continuous analogs of the resultant operator.

Contribution

It introduces explicit formulas for matrix-valued accelerants with discontinuities in Krein systems, expanding the theoretical framework and applications.

Findings

Explicit formulas for accelerants with jumps

Extension of Krein system spectral theory

Use of continuous analogs of the resultant operator

Abstract

In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role.