Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials

We improve results by Frank, Hainzl, Naboko, and Seiringer (J Geom Anal 17(4):559–567, 2007) and Hainzl and Seiringer (Math Nachr 283(3):489–499, 2010) on the weak coupling limit of eigenvalues for Schrödinger-type operators whose kinetic energy vanishes on a codimension one submanifold. The main te...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 111; no. 2
Main Authors Cuenin, Jean-Claude, Merz, Konstantin
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2021
Springer Nature B.V
Subjects
Complex Systems
Coupling
Eigenvalues
Geometry
Group Theory and Generalizations
Kinetic energy
Manifolds (mathematics)
Mathematical and Computational Physics
Operators
Physics
Physics and Astronomy
Theoretical
Eigenvalue asymptotics
Tomas-Stein theorem
Fourier restriction
Secondary: 81Q10
Degenerate kinetic energy
Weak coupling limit
Primary: 58C40
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Summary:We improve results by Frank, Hainzl, Naboko, and Seiringer (J Geom Anal 17(4):559–567, 2007) and Hainzl and Seiringer (Math Nachr 283(3):489–499, 2010) on the weak coupling limit of eigenvalues for Schrödinger-type operators whose kinetic energy vanishes on a codimension one submanifold. The main technical innovation that allows us to go beyond the potentials considered in Frank, Hainzl, Naboko, and Seiringer (2007), Hainzl and Seiringer (2010) is the use of the Tomas–Stein theorem.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01385-2