Krein's strings whose spectral functions are of polynomial growth

TL;DR

This paper establishes a necessary and sufficient condition for the continuity of Krein's correspondence specifically for Krein's strings with spectral functions exhibiting polynomial growth.

Contribution

It provides a precise criterion linking spectral function growth to the continuity of Krein's spectral correspondence.

Findings

Characterization of spectral functions with polynomial growth

Necessary and sufficient condition for Krein's correspondence continuity

Enhanced understanding of spectral properties of Krein's strings

Abstract

In the case of Krein's strings with spectral functions of polynomial growth a necessary and sufficient condition for the Krein's correspondence to be continuous is given.