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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1162–1175 (Mi izv2511)  

This article is cited in 15 scientific papers (total in 15 papers)

The existence of wave operators in scattering theory for pairs of spaces

A. L. Belopol'skii, M. Sh. Birman

Abstract: Existence conditions are considered for wave operators for pairs of self-adjoint operators which act in different Hilbert spaces. The “operator of identification” is not assumed to be isometric. The existence criteria obtained for wave operators (local and nonlocal) are related to perturbation theory of nuclear operators. The construction of wave operators is carried out by a stationary method.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1117–1130

Bibliographic databases:

UDC: 517.9
MSC: 47A40, 47B25, 47A55
Received: 20.03.1968

Citation: A. L. Belopol'skii, M. Sh. Birman, “The existence of wave operators in scattering theory for pairs of spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1162–1175; Math. USSR-Izv., 2:5 (1968), 1117–1130

Citation in format AMSBIB
\by A.~L.~Belopol'skii, M.~Sh.~Birman
\paper The existence of wave operators in scattering theory for pairs of
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 5
\pages 1162--1175
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1117--1130

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    This publication is cited in the following articles:
    1. M. Sh. Birman, “A local criterion for the existence of wave operators”, Math. USSR-Izv., 2:4 (1968), 879–906  mathnet  crossref  mathscinet  zmath
    2. M. Sh. Birman, “Scattering problems for differential operators with perturbation of the space”, Math. USSR-Izv., 5:2 (1971), 459–474  mathnet  crossref  mathscinet  zmath
    3. A. L. Belopol'skii, “Scattering problems for two spaces with an unbounded identification operator”, Funct. Anal. Appl., 5:2 (1971), 151–152  mathnet  crossref  mathscinet  zmath
    4. V. B. Matveev, M. M. Skriganov, “Scattering problem for radial Schrödinger equation with a slowly decreasing potential”, Theoret. and Math. Phys., 10:2 (1972), 156–164  mathnet  crossref  zmath
    5. V. B. Matveev, “Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential”, Theoret. and Math. Phys., 15:3 (1973), 574–583  mathnet  crossref
    6. B. S. Pavlov, “Calculating losses in scattering problems”, Math. USSR-Sb., 26:1 (1975), 71–87  mathnet  crossref  mathscinet  zmath
    7. Colston Chandler, A. G. Gibson, “N-body quantum scattering theory in two Hilbert spaces. I. The basic equations”, J Math Phys (N Y ), 18:12 (1977), 2336  crossref  mathscinet  adsnasa
    8. D.B Pearson, “A generalization of the Birman trace theorem”, Journal of Functional Analysis, 28:2 (1978), 182  crossref
    9. M. Combescure, J. Ginibre, “Scattering and local absorption for the Schrödinger operator”, Journal of Functional Analysis, 29:1 (1978), 54  crossref
    10. V. D. Koshmanenko, “Haag–Ruelle scattering theory as scattering theory in different state spaces”, Theoret. and Math. Phys., 38:2 (1979), 109–119  mathnet  crossref  mathscinet
    11. Yu. G. Shondin, “Generalized pointlike interactions in $R_3$ and related models with rational $S$-matrix”, Theoret. and Math. Phys., 64:3 (1985), 937–944  mathnet  crossref  mathscinet  isi
    12. Arvind B Patel, “On the scattering theorems of Pearson and Ismagilov”, Journal of Functional Analysis, 88:1 (1990), 228  crossref
    13. Rolf Leis, “Variations on the wave equation”, Math Meth Appl Sci, 24:6 (2001), 339  crossref  mathscinet  zmath  isi
    14. M. Z. Solomyak, T. A. Suslina, D. R. Yafaev, “On the mathematical works of M. Sh. Birman”, St. Petersburg Math. J., 23:1 (2012), 1–38  mathnet  crossref  mathscinet  zmath  isi  elib
    15. R. Leis, G. F. Roach, “A transmission problem for the plate equation”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 99:3-4 (2011), 285  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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