ON THE SPECTRAL PROPERTIES OF DISCRETE SCHRÖDINGER OPERATORS

1999 ◽  
Vol 11 (09) ◽  
pp. 1061-1078 ◽  
Author(s):  
ANNE BOUTET DE MONVEL ◽  
JAOUAD SAHBANI
Keyword(s):  
Large Class ◽  
Continuous Spectrum ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
Decay Estimates ◽  
Singular Continuous Spectrum ◽  
Conjugate Operator ◽  
Discrete Schrödinger Operator ◽  
Limiting Absorption Principle ◽  
Discrete Schrödinger Operators

We use the method of the conjugate operator to prove the limiting absorption principle and the absence of the singular continuous spectrum for the discrete Schrödinger operator. We also obtain local decay estimates. Our results apply to a large class of perturbating potentials V tending arbitrarily slowly to zero at infinity.

Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends

1997 ◽  
Vol 49 (2) ◽  
pp. 232-262 ◽  
Author(s):  
Julian Edward
Keyword(s):  
Large Class ◽  
Continuous Spectrum ◽  
Spectral Theory ◽  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Singular Continuous Spectrum ◽  
Finite Multiplicity ◽  
Planar Domains ◽  
Neumann Laplacian

AbstractThe spectral theory for the Neumann Laplacian on planar domains with symmetric, horn-like ends is studied. For a large class of such domains, it is proven that the Neumann Laplacian has no singular continuous spectrum, and that the pure point spectrum consists of eigenvalues of finite multiplicity which can accumulate only at 0 or ∞. The proof uses Mourre theory.

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