# A Riesz basis criterion for Schr\"odinger operators with boundary conditions dependent on the eigenvalue parameter

## TL;DR

This paper provides a criterion to determine when eigenfunctions of a one-dimensional Schrödinger operator with distributional potentials and eigenvalue-dependent boundary conditions form a Riesz basis in L2(0,π).

## Contribution

It introduces a new Riesz basis criterion for Schrödinger operators with boundary conditions depending on the eigenvalue parameter.

## Key findings

- Established a Riesz basis criterion for eigenfunctions.
- Applicable to operators with distributional potentials.
- Enhances understanding of spectral properties of such operators.

## Abstract

We establish a criterion for a set of eigenfunctions of the one-dimensional Schr\"{o}dinger operator with distributional potentials and boundary conditions containing the eigenvalue parameter to be a Riesz basis for $\mathscr{L}_2(0,\pi)$.