Schrödinger operators with slowly decaying Wigner–von Neumann type potentials

Milivoje Lukic

doi:10.4171/jst/41

Schrödinger operators with slowly decaying Wigner–von Neumann type potentials

Journal of Spectral Theory ◽

10.4171/jst/41 ◽

2013 ◽

Vol 3 (2) ◽

pp. 147-169 ◽

Cited By ~ 10

Author(s):

Milivoje Lukic

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Von Neumann ◽

Neumann Type

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Wigner-von Neumann type perturbations of periodic Schrödinger operators

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-2014-06365-4 ◽

2014 ◽

Vol 367 (1) ◽

pp. 707-724 ◽

Cited By ~ 5

Author(s):

Milivoje Lukic ◽

Darren C. Ong

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Von Neumann ◽

Neumann Type

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On Schrödinger operators with von Neumann-Wigner type potentials

Lecture Notes in Mathematics - Differential Equations and Mathematical Physics ◽

10.1007/bfb0080584 ◽

1987 ◽

pp. 91-98 ◽

Cited By ~ 1

Author(s):

Allen Devinatz ◽

Richard Moeckel ◽

Peter Rejto

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Von Neumann

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A Turning Point Problem Arising in Connection with a Limiting Absorption Principle for Schrödinger Operators with Generalized Von Neumann—Wigner Potentials

Spectral and Scattering Theory ◽

10.1007/978-1-4899-1552-8_9 ◽

1998 ◽

pp. 131-155

Author(s):

Peter Rejto ◽

Mario Taboada

Keyword(s):

Turning Point ◽

Schrödinger Operators ◽

Point Problem ◽

Schrodinger Operators ◽

Limiting Absorption Principle ◽

Von Neumann

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Limiting Absorption Principle for Discrete Schrödinger Operators with a Wigner–von Neumann Potential and a Slowly Decaying Potential

Annales Henri Poincaré ◽

10.1007/s00023-020-00971-9 ◽

2020 ◽

Author(s):

Sylvain Golénia ◽

Marc-Adrien Mandich

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Limiting Absorption Principle ◽

Von Neumann ◽

Discrete Schrödinger Operators

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A Limiting Absorption Principle for Schrödinger Operators with Generalized Von Neumann–Wigner Potentials I. Construction of Approximate Phase

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1997.5293 ◽

1997 ◽

Vol 208 (1) ◽

pp. 85-108 ◽

Cited By ~ 6

Author(s):

Peter Rejto ◽

Mario Taboada

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Limiting Absorption Principle ◽

Von Neumann

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A Limiting Absorption Principle for Schrödinger Operators with Generalized Von Neumann–Wigner Potentials II. The Proof

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1997.5294 ◽

1997 ◽

Vol 208 (2) ◽

pp. 311-336 ◽

Cited By ~ 4

Author(s):

Peter Rejto ◽

Mario Taboada

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Limiting Absorption Principle ◽

Von Neumann

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The Krein–von Neumann Extension for Schrödinger Operators on Metric Graphs

Complex Analysis and Operator Theory ◽

10.1007/s11785-020-01076-1 ◽

2021 ◽

Vol 15 (2) ◽

Author(s):

Jacob Muller ◽

Jonathan Rohleder

Keyword(s):

Schrödinger Operators ◽

Schrodinger Operators ◽

Metric Graphs ◽

Von Neumann ◽

Metric Graph

AbstractThe Krein–von Neumann extension is studied for Schrödinger operators on metric graphs. Among other things, its vertex conditions are expressed explicitly, and its relation to other self-adjoint vertex conditions (e.g. continuity-Kirchhoff) is explored. A variational characterisation for its positive eigenvalues is obtained. Based on this, the behaviour of its eigenvalues under perturbations of the metric graph is investigated, and so-called surgery principles are established. Moreover, isoperimetric eigenvalue inequalities are obtained.

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