Basis properties of Fucik eigenfunctions

TL;DR

This paper investigates conditions under which Fucik eigenfunctions of the 1D Laplacian form a Riesz basis in L^2(0,π), providing theoretical guarantees for their basis properties.

Contribution

It introduces sufficient assumptions on Fucik eigenvalues that ensure the eigenfunctions form a Riesz basis, advancing understanding of their spectral properties.

Findings

Established conditions guaranteeing Riesz basis formation

Provided new theoretical insights into Fucik eigenfunctions

Enhanced spectral analysis of the 1D Laplacian

Abstract

We establish sufficient assumptions on sequences of Fucik eigenvalues of the one-dimensional Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\pi)$.