Spectral estimates for Schrödinger operators with sparse potentials on graphs
Journal article, 2011

A construction of "sparse potentials," suggested by the authors for the lattice ℤd, d gt; 2, is extended to a large class of combinatorial and metric graphs whose global dimension is a number D gt; 2. For the Schrödinger operator - Δ - αV on such graphs, with a sparse potential V, we study the behavior (as α → ∞) of the number N_(-Δ - αV) of negative eigenvalues of - Δ - αV. We show that by means of sparse potentials one can realize any prescribed asymptotic behavior of N_(-Δ - αV) under very mild regularity assumptions. A similar construction works also for the lattice ℤ2, where D = 2.

Eigenvalue estimates

Quantum graphs

Shchrödinger operators


Grigori Rozenblioum

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Michael Solomyak

Weizmann Institute of Science

Journal of Mathematical Sciences

1072-3374 (ISSN)

Vol. 176 3 458-474


Basic sciences

Subject Categories

Mathematical Analysis



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