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Invariant Subspace Theorems for Finite Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Morisuke Hasumi
Morisuke Hasumi*
Affiliation:
Ibaraki University, Mito, Japan and University of California, Berkeley
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The purpose of this paper is to extend various invariant subspace theorems for the circle group to multiply connected domains. Such attempts are not new. Actually, Sarason (4) studied the invariant subspaces of annulus operators acting on L2 and showed certain parallelisms between the unit disk case and the annulus case. Voichick (8) observed analytic functions on a finite Riemann surface and generalized the Beurling theorem on the closed invariant subspaces of H2 as well as the Beurling–Rudin theorem on the closed ideals of the disk algebra. Here we shall consider LP(Γ) and C(Γ) defined on the boundary Γ of a finite orientable Riemann surface R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 240 - 255
Copyright
Copyright © Canadian Mathematical Society 1966

References

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