On spectral estimates for Schrödinger-type operators: the case of small local dimension

DOI10.1007/s10688-010-0037-7zbMath1272.47055arXiv1005.2690OpenAlexW2080884480MaRDI QIDQ366264

Grigori Rozenblum, Michael Solomyak

Publication date: 12 September 2013

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.2690

zbMATH Keywords

Schrödinger operatorlocal dimensioneigenvalue estimatesmetric graphdimension at infinity

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (11)

Infinite quantum graphs ⋮ On spectral estimates for the Schrödinger operators in global dimension 2 ⋮ Sobolev-type inequalities and eigenvalue growth on graphs with finite measure ⋮ Laplacians on infinite graphs: discrete vs. continuous ⋮ Quantitative bounds versus existence of weakly coupled bound states for Schrödinger type operators ⋮ Bounds on the discrete spectrum of lattice Schrödinger operators ⋮ Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph ⋮ Spectral theory of infinite quantum graphs ⋮ On the mathematical work of Mikhail Zakharovich Solomyak ⋮ Spectral estimates for Schrödinger operators with sparse potentials on graphs ⋮ Negative eigenvalues of two-dimensional Schrödinger operators

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