Spectral representation of local semigroups associated with Klein-Landau systems
1984 ◽
Vol 95
(1)
◽
pp. 93-100
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Keyword(s):
In their paper [5], Klein and Landau prove that given a symmetric ‘local semigroup’ of unbounded operators {T(t); t ≥ 0} on a Hilbert space, there exists a unique selfadjoint operator T such that T(t) is a restriction of e−tT, for each t ≥ 0. A similar representation theorem was proved earlier by Nussbaum [8]. The result of Klein and Landau was recently extended to the setting of reflexive Banach spaces by Kantorovitz ([4], theorem 2–3). More precisely, Kantorovitz presented necessary and sufficient conditions for a local semigroup of unbounded operators {T(t); t ≥ 0} to consist of restrictions of e−tT, t ≥ 0, for some unbounded spectral operator of scalar-type T with real spectrum (cf. [1] for the terminology).
1992 ◽
Vol 04
(spec01)
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pp. 15-47
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2004 ◽
Vol 2004
(45)
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pp. 2401-2422
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1985 ◽
Vol 26
(2)
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pp. 177-180
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1980 ◽
Vol 35
(4)
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pp. 437-441
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2009 ◽
Vol 2009
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pp. 1-11
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