Cauchy-type integrals and singular measures

Kapustin, V.

doi:10.1090/S1061-0022-2013-01263-5

Cauchy-type integrals and singular measures
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by V. V. Kapustin
Translated by: the author

St. Petersburg Math. J. 24 (2013), 743-757

DOI: https://doi.org/10.1090/S1061-0022-2013-01263-5

Published electronically: July 24, 2013

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Abstract:

In an earlier paper by the author it was shown that, in the case of rank-two commutators the problem of existence of an averaged wave operator for a pair of unitary operators whose spectral measures are singular with respect to the Lebesgue measure can be rewritten in terms of Cauchy-type integrals. The approach to the problem presented in the paper is based upon truncated Toeplitz operators, convergence is analyzed in terms of their symbols, and the results obtained are applied to the boundary behavior of functions belonging to $\ast$-invariant subspaces of the Hardy class $H^2$.

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