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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Boundary values of Cauchy type integrals

Author: V. V. Kapustin
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 4.
Journal: St. Petersburg Math. J. 16 (2005), 691-702
MSC (2000): Primary 30E20, 47B47
Published electronically: June 23, 2005
MathSciNet review: 2090853
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Abstract | References | Similar Articles | Additional Information

Abstract: Results by A. G. Poltoratskii and A. B. Aleksandrov about nontangential boundary values of pseudocontinuable $H^2$-functions on sets of zero Lebesgue measure are used for the study of operators on $L^2$-spaces on the unit circle. For an arbitrary bounded operator $X$ acting from one such $L^2$-space to another and having the property that the commutator of it with multiplication by the independent variable is a rank one operator, it is shown that $X$ can be represented as a sum of multiplication by a function and a Cauchy transformation in the sense of angular boundary values.

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Additional Information

V. V. Kapustin
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Keywords: Cauchy type integral, angular boundary values, intertwining relations
Received by editor(s): January 20, 2004
Published electronically: June 23, 2005
Additional Notes: Partially supported by RFBR (grant no. 02–01–00264), and by the SS grant no. 2266.2003.1.
Article copyright: © Copyright 2005 American Mathematical Society