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Bound states and scattered states for contraction semigroups (1985)

Goldstein, Jerome A.

Springer

Acta applicandae mathematicae 4 (1985), S. 93-98

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ISSN: 1572-9036

Keywords: Primary ; 47D05 ; secondary ; 34G10 ; 35P25 ; 47D45 ; RAGE theorem ; contraction semigroups ; asymptotics ; bound state ; scattered state ; mean ergodic theorem ; Wiener's theorem ; almost convergence

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract LetA generate a strongly continuous contraction semigroup {T(t)} on a Hilbert space and letL be a bounded operator. IfL(ζI−A)−1 is compact, then the Cesàro limit of ‖LT(t)f‖2 (ast→∞) is computed for all vectorsf. This limit is interpreted in terms of bound and scattered states in the context of quantum mechanical and classical wave propagation problems.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02293492

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