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Invariant Subspaces on Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Michael Voichick
Michael Voichick*
Affiliation:
Dartmouth College, University of Wisconsin
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In this paper we generalize to Riemann surfaces a theorem of Helson and Lowdenslager in (2) describing the closed subspaces of L2(﹛|z| = 1﹜) that are invariant under multiplication by eiθ.

Let R be a region on a Riemann surface with boundary Γ consisting of a finite number of disjoint simple closed analytic curves such that R ⋃ Γ is compact and R lies on one side of Γ. Let dμ be the harmonic measure on Γ with respect to a fixed point t0 on R. We shall consider the closed subspaces of L2(Γ, dμ) that are invariant under multiplication by functions in A (R) = ﹛F|F continuous on , analytic on R}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 399 - 403
Copyright
Copyright © Canadian Mathematical Society 1966

References

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