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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 389, Pages 5–20
(Mi znsl4115)
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This article is cited in 4 scientific papers (total in 4 papers)
The future and past wave operators on the singular spectrum
R. V. Bessonov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
We consider averaged wave operators constructed for singular unitary operators $U_1$, $U_2$ and a bounded identification operator $A$. In the case of rank-two commutator $AU_1-U_2A$, we show that averaged wave operators of past and future exist or do not exist simultaneously, and if they exist, they must coincide. As a consequence, we obtain some results concerning the boundary behavior of Cauchy-type integrals.
Key words and phrases:
wave operator, summation methods, singular spectral measure.
Received: 24.06.2011
Citation:
R. V. Bessonov, “The future and past wave operators on the singular spectrum”, Investigations on linear operators and function theory. Part 39, Zap. Nauchn. Sem. POMI, 389, POMI, St. Petersburg, 2011, 5–20; J. Math. Sci. (N. Y.), 182:5 (2012), 587–594
Linking options:
https://www.mathnet.ru/eng/znsl4115 https://www.mathnet.ru/eng/znsl/v389/p5
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Abstract page: | 272 | Full-text PDF : | 86 | References: | 53 |
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