Spectral asymptotics for the Schrödinger operator with a non-decaying potential
Keyword(s):
We study Schrödinger operators H ( h ) = − h 2 Δ + V ( x ) acting in L 2 ( R n ) for non-decaying potentials V. We give a full asymptotic expansion of the spectral shift function for a pair of such operators in the high energy limit. In particular for asymptotically homogeneous potentials W at infinity of degree zero, we also study the semiclassical asymptotics to give a Weyl formula of the spectral shift function above the threshold max W and Mourre estimates in the range of W except at its critical values.
2004 ◽
Vol 45
(9)
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pp. 3453-3461
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2002 ◽
Vol 27
(11-12)
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pp. 2139-2186
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Keyword(s):
Keyword(s):
2007 ◽
Vol 19
(10)
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pp. 1071-1115
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1996 ◽
Vol 24
(3)
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pp. 285-297
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1973 ◽
Vol 6
(2)
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pp. 236-246