Abstract
In the paper one proves that a measurable partition of the circumference is induced by an inner function if and only if the corresponding operator of conditional mathematical expectation commutes with the M. Riesz projection.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. A. Rokhlin, “On the fundamental concepts of measure theory,” Mat. Sb.,25 (67), 107–150 (1949).
P. Koosis, Introduction to Hp Spaces. With an Appendix on Wolff's Proof of the Corona Theorem, Cambridge Univ. Press (1980).
A. B. Aleksandrov, “The multiplicity of boundary values of inner functions,” Izv. Akad. Nauk ArmSSR, Ser. Mat.,20, No. 6, 416–427 (1985).
S. V. Hruscev, N. K. Nikol'skii, and B. S. Pavlov, “Unconditional bases of exponentials and of reproducing kernels,” Lect. Notes Math., No. 864, 214–335 (1981).
S. V. Hruscev and S. A. Vinogradov, “Free interpolation in the space of uniformly convergent Taylor series,” Lect. Notes Math., No. 864, 171–213 (1981).
N. K. Nikol'skii, Lectures on the Shift Operator [in Russian], Nauka, Moscow (1980).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 103–106, 1986.
Rights and permissions
About this article
Cite this article
Aleksandrov, A.B. Measurable partitions of the circumference, induced by inner functions. J Math Sci 42, 1610–1613 (1988). https://doi.org/10.1007/BF01665047
Issue Date:
DOI: https://doi.org/10.1007/BF01665047