Regularity of dissipative operators

TL;DR

This paper proves S.G. Krein's conjecture for Birkhoff-regularity of dissipative differential operators of even order, establishing the existence of a characteristic matrix limit and its relation to regularity determinants.

Contribution

It confirms Krein's conjecture for even order cases and links the characteristic matrix limit to regularity determinants.

Findings

Proof of Krein's conjecture for even order dissipative operators

Existence of the characteristic matrix limit in the lower half-plane

Limit coincides with the ratio of regularity determinants matrices

Abstract

S.G.Krein's conjecture concerning Birkhoff-regularity of dissipative differential operators has been proved in the even order case. As a byproduct an existence of the limit of characteristic matrix as in the lower half-plane has been established. Up to multiplication by a nonvanishing matrix this limit coincides with the ratio of the matrices of regularity determinants.