Geodesic
The future and past wave operators on the singular spectrum
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 5-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {R. V. Bessonov},
     title = {The future and past wave operators on the singular spectrum},
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}
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R. V. Bessonov. The future and past wave operators on the singular spectrum. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 5-20. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a0/

[1] D. R. Yafaev, Matematicheskaya teoriya rasseyaniya, Izd-vo SPbGU, S.-Peterburg, 1994 | MR

[2] V. V. Kapustin, “Granichnye znacheniya integralov tipa Koshi”, Algebra i Analiz, 16:4 (2004), 114–131 | MR | Zbl

[3] V. V. Kapustin, “Volnovye operatory na singulyarnom spektre”, Zap. nauchn. semin. POMI, 376, 2010, 48–63 | MR

[4] V. V. Kapustin, Wave operators on the singular spectrum. The case of rank-two commutators, Preprint 06/2010, PDMI

[5] V. V. Kapustin, On the averaged wave operators on the singular spectrum, Preprint 08/2011, PDMI

[6] A. G. Poltoratskii, “Granichnoe povedenie psevdoprodolzhimykh funktsii”, Algebra i Analiz, 5:2 (1993), 189–210 | MR | Zbl

[7] D. Clark, “One dimensional perturbations of restricted shifts”, J. Anal. Math., 25 (1972), 169–191 | DOI | MR | Zbl

[8] A. B. Aleksandrov, “Invariantnye podprostranstva operatorov sdviga. Aksiomaticheskii podkhod”, Zapiski nauchn. semin. LOMI, 113, 1981, 7–26 | MR | Zbl

[9] J. A. Cima, A. L. Matheson, W. T. Ross, The Cauchy Transform, Mathematical Surveys and Monographs, 125, American Mathematical Society, Providence, RI, 2006 | DOI | MR | Zbl