SHARP SPECTRAL ESTIMATES IN DOMAINS OF INFINITE VOLUME
2011 ◽
Vol 23
(06)
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pp. 615-641
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Keyword(s):
We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume — and therefore on the volume of the domain — must fail. Here we present a method on how one can nevertheless prove uniform bounds on eigenvalues and eigenvalue means which are sharp in the semiclassical limit.We give examples in horn-shaped regions and so-called spiny urchins. Some results are extended to Schrödinger operators defined on quasi-bounded domains with Dirichlet boundary conditions.
2010 ◽
Vol 88
(3)
◽
pp. 320-330
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2014 ◽
Vol 11
(05)
◽
pp. 1450040
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Keyword(s):
Keyword(s):
2009 ◽
Vol 103
(3)
◽
pp. 209-225
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2017 ◽
Vol 45
◽
pp. 1760021
Keyword(s):
1969 ◽
Vol 69
(1)
◽
pp. 77-88
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2002 ◽
Vol 74
(1-2)
◽
pp. 349-370
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1964 ◽
Vol 36
(2)
◽
pp. 595-609
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