Nonharmonic analysis of boundary value problems without WZ condition

TL;DR

This paper extends nonharmonic analysis of boundary value problems by relaxing eigenfunction zero-free conditions and boundedness assumptions, broadening the applicability of pseudo-differential analysis.

Contribution

It introduces a generalized framework for nonharmonic analysis that accommodates eigenfunctions with zeros and unbounded domains, advancing the theoretical foundation.

Findings

Extended analysis to eigenfunctions with zeros

Applicable to unbounded domains

Broadened scope of pseudo-differential analysis

Abstract

In this work we continue our research on nonharmonic analysis of boundary value problems as initiated in our recent paper (IMRN 2016). There, we assumed that the eigenfunctions of the model operator on which the construction is based do not have zeros. In this paper we have weakened this condition extending the applicability of the developed pseudo-differential analysis. Also, we do not assume that the underlying set is bounded.