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Spectral estimates for Schrödinger operators with sparse potentials on graphs

Michael Solomyak ; Grigori Rozenblioum (Institutionen för matematiska vetenskaper, matematik)
Journal of Mathematical Sciences (10723374). Vol. 176 (2011), 3, p. 458-474.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Shchrödinger operators, Quantum graphs, Eigenvalue estimates

Denna post skapades 2011-12-22.
CPL Pubid: 150907


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Matematisk analys

Chalmers infrastruktur