Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2204.06244

Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian

Falko Baustian·Vladimir Bobkov
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,π)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fucik eigenvalues which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,π)$ and we explicitly describe the corresponding biorthogonal system.

Explore related subjects

math.CAmath.APmath.SP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Falko Baustian, Vladimir Bobkov. 2022-04-13. Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian. https://doi.org/10.1016/j.jmaa.2022.126466

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Weighted inequalities in ergodic theory via transference

We first extend Calderón's transfer principle to weighted spaces in various different settings under suitable assumptions. Then we apply our results for some inequalities on the real line obtained by the author to prove corresponding inequalities in ergodic theory and ergodic $H^1$ spaces as well.

math.CA↗
arXiv2026

Wavelet resolution and Sobolev regularity of Calderón-Zygmund operators on domains

Given a uniform domain $Ω\subset {\mathbb R}^d$, we resolve each element of a suitably defined class of Calderòn-Zygmund (CZ) singular integrals on $Ω$ as the linear combination of Triebel wavelet operators and paraproduct terms. Our resolution formula entails a testing type characterization, loosely in the vein of the David-Journé theorem, of weighted Sobolev space bounds in terms of Triebel-Lizorkin and tree Carleson measure norms of the paraproduct symbols, which is new already in the case $Ω={\mathbb R}^d$ with Lebesgue measure. Our characterization covers the case of compressions to $Ω$ of global CZ operators, extending and sharpening past results of Prats and Tolsa for the convolution case. The weighted estimates we obtain, particularized to the Beurling operator on a Lipschitz domain with normal to the boundary in the corresponding sharp Besov class, may be used to deduce quantitative estimates for quasiregular mappings with dilatation in the Sobolev space $W^{1,p}(Ω)$, $p>2$.

math.CA↗