A short proof of Weyl's law for fractional differential operators

DOI10.1063/1.4861935zbMath1317.35158arXiv1309.1867OpenAlexW3099326475MaRDI QIDQ5414737

Leander Geisinger

Publication date: 7 May 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1867

zbMATH Keywords

spectral asymptoticsWeyl's lawfractional differential operators

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Fractional partial differential equations (35R11)

Related Items (12)

A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions ⋮ Regularity theory for general stable operators: parabolic equations ⋮ Spectral Properties of the logarithmic Laplacian ⋮ On the Weyl law for quantum graphs ⋮ Regularity estimates for nonlocal Schrödinger equations ⋮ Spectral properties of the logarithmic Laplacian ⋮ Spectral results for mixed problems and fractional elliptic operators ⋮ Estimates the upper bounds of Dirichlet eigenvalues for fractional Laplacian ⋮ On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians ⋮ Singular solutions for fractional parabolic boundary value problems ⋮ On the spectral asymptotics for the buckling problem ⋮ Boundary regularity for the fractional heat equation

Cites Work

• Refined semiclassical asymptotics for fractional powers of the Laplace operator
• Hitchhiker's guide to the fractional Sobolev spaces
• On the Schrödinger equation and the eigenvalue problem
• The asymptotic distribution of the eigenvalues for a class of Markov operators
• Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
• Geometrical versions of improved Berezin-Li-Yau inequalities
• The classical limit of quantum spin systems
• ESTIMATES FOR THE SUMS OF EIGENVALUES OF THE FRACTIONAL LAPLACIAN ON A BOUNDED DOMAIN
• Refined bounds for the eigenvalues of the Klein-Gordon operator
• Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain
• BOUNDS FOR THE EIGENVALUES OF THE FRACTIONAL LAPLACIAN
• A century of complex Tauberian theory
• Improved Berezin-Li-Yau inequalities with a remainder term
• A lower bound for sums of eigenvalues of the Laplacian
• Spectral properties of the Dirichlet operator $\sum _{i=1}^{d}(-\partial _i^2)^{s}$∑i=1d(−∂i2)s on domains in d-dimensional Euclidean space
• Remarks on eigenvalue estimates and semigroup domination
• Two-dimensional Berezin-Li-Yau inequalities with a correction term
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