, Volume 61, Issue 2, pp 2046-2056

Invariant subspaces of the operator of multiplication by z in the space Ep in a multiply connected domain

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Abstract

In the paper one obtains the description of invariant subspaces of the multiplication operator in the Hardy-Smirnov space Ep (G), where G is afinitely connected domain with a piecewise C2-smooth boundary. For the case of an analytic “interior boundary” Γint of the domain G and p=2, a more precise description is given, generalizing the Hitt—Sarason result on the invariant subspaces of the space H2 in a circular annulus.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 166–183, 1989.
The author is grateful to N. K. Nikol'skii for his constant interest in this paper and to V. I. Vasyunin, A. L. Vol'berg, and V. M. Solomyak for useful discussions and remarks.