A Weighted Dispersive Estimate for Schrödinger Operators in Dimension Two

Let H  = −Δ +  V , where V is a real valued potential on satisfying . We prove that if zero is a regular point of the spectrum of H  = −Δ +  V , then , with w ( x ) = (log(2 + | x |)) 2 . This decay rate was obtained by Murata in the setting of weighted L 2 spaces with polynomially growing weights....

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Bibliographic Details
Published in:Communications in mathematical physics 2013-05, Vol.319 (3), p.791-811
Main Authors: Erdoğan, M. Burak, Green, William R.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:Let H  = −Δ +  V , where V is a real valued potential on satisfying . We prove that if zero is a regular point of the spectrum of H  = −Δ +  V , then , with w ( x ) = (log(2 + | x |)) 2 . This decay rate was obtained by Murata in the setting of weighted L 2 spaces with polynomially growing weights.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-012-1640-7