scholarly journals Spectral Asymptotics for Schrödinger Operators with Periodic Point Interactions

2002 ◽  
Vol 266 (1) ◽  
pp. 127-148 ◽  
Author(s):  
P. Kurasov ◽  
J. Larson
Keyword(s):  
Periodic Point ◽  
Schrödinger Operators ◽  
Spectral Asymptotics ◽  
Schrodinger Operators ◽  
Point Interactions

scholarly journals Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori

2022 ◽  
Vol 216 ◽  
pp. 112679
Author(s):  
Dario Bambusi ◽  
Beatrice Langella ◽  
Riccardo Montalto
Keyword(s):  
Schrödinger Operators ◽  
Spectral Asymptotics ◽  
Schrodinger Operators ◽  
Flat Tori

scholarly journals Two-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators

2019 ◽  
Vol 31 (04) ◽  
pp. 1950012 ◽  
Author(s):  
Horia D. Cornean ◽  
Alessandro Michelangeli ◽  
Kenji Yajima
Keyword(s):  
Schrödinger Operators ◽  
Sufficient Conditions ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
Point Interactions ◽  
Wave Operators ◽  
Regular Type ◽  
Local Point ◽  
Embedded Eigenvalue ◽  
Necessary And Sufficient

We study the threshold behavior of two-dimensional Schrödinger operators with finitely many local point interactions. We show that the resolvent can either be continuously extended up to the threshold, in which case we say that the operator is of regular type, or it has singularities associated with [Formula: see text] or [Formula: see text]-wave resonances or even with an embedded eigenvalue at zero, for whose existence we give necessary and sufficient conditions. An embedded eigenvalue at zero may appear only if we have at least three centers. When the operator is of regular type, we prove that the wave operators are bounded in [Formula: see text] for all [Formula: see text]. With a single center, we always are in the regular type case.

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