Journal of Mathematical Sciences

, Volume 172, Issue 2, pp 207–214 | Cite as

On wave operators on the singular spectrum


The problem of existence of a wave operator is considered in the general case where the spectral measures of the unitary operators are not assumed to be absolutely continuous. The case of commutators of rank at most two is studied in more detail. Bibliography: 6 titles.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. R. Yafaev, Mathematical Scattering Theory [in Russian], St. Petersburg (1994).Google Scholar
  2. 2.
    V. V. Kapustin, PDMIP reprint 06/2010.Google Scholar
  3. 3.
    G. Hardy, Divergent Series [Russian translation], Moscow (1951).Google Scholar
  4. 4.
    V. V. Kapustin, “Boundary values of Cauchy-type integrals,” Algebra Analiz, 16, 114–131 (2004).MathSciNetGoogle Scholar
  5. 5.
    D. N. Clark, “One-dimensional perturbations of restricted shifts,” J. Anal. Math., 25, 169–191 (1972).MATHCrossRefGoogle Scholar
  6. 6.
    A. G. Poltoratskii, “Boundary behavior of pseudocontinuable functions,” Algebra Analiz, 5, 189–210 (1993).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

Personalised recommendations