Functional Analysis and Its Applications

, Volume 46, Issue 2, pp 100–109

Averaged wave operators on singular spectrum


DOI: 10.1007/s10688-012-0016-2

Cite this article as:
Kapustin, V.V. Funct Anal Its Appl (2012) 46: 100. doi:10.1007/s10688-012-0016-2


We prove the existence of pairs of unitary (or self-adjoint) operators with singular spectral measure whose difference is a rank-two operator for which the Abel wave operators fail to exist. Also, we discuss the closely related problem of constructing the Hilbert transform with respect to a singular measure on the unit circle.

Key words

wave operator summation methods singular measure Hilbert transform 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical Institute RASSt. PetersburgRussia

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