Basisness of Fucik eigenfunctions for the Dirichlet Laplacian

TL;DR

This paper establishes new conditions under which Fucik eigenfunctions of the 1D Dirichlet Laplacian form a Riesz basis in L^2(0,π), enhancing understanding of their basis properties.

Contribution

It introduces improved sufficient assumptions on Fucik eigenvalues ensuring the eigenfunctions form a Riesz basis, along with a new criterion for Riesz basis in Hilbert spaces.

Findings

Provided new sufficient conditions for Riesz basis formation.

Introduced a novel criterion for sequences to be Riesz bases.

Enhanced the theoretical understanding of Fucik eigenfunctions.

Abstract

We provide improved sufficient assumptions on sequences of Fucik eigenvalues of the one-dimensional Dirichlet Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\pi)$. For that purpose, we introduce a criterion for a sequence in a Hilbert space to be a Riesz basis.