Optimization of quasi-normal eigenvalues for Krein-Nudelman strings

TL;DR

This paper addresses the optimization of resonances in Krein strings under mass and moment constraints, explicitly identifying optimal resonances and corresponding strings to minimize the imaginary part of the resonance.

Contribution

It provides explicit solutions for the optimal resonances and strings in the context of Krein strings with specified constraints, advancing the understanding of resonance optimization.

Findings

Explicit formulas for optimal resonances and strings

Minimal imaginary part achieved for given real part 

Resonance design under mass and moment constraints

Abstract

The paper is devoted to optimization of resonances for Krein strings with total mass and statical moment constraints. The problem is to design for a given $\alpha \in \R$ a string that has a resonance on the line $\alpha + \i \R$ with a minimal possible modulus of the imaginary part. We find optimal resonances and strings explicitly.