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Invariant subspaces on open Riemann surfaces

Morisuke Hasumi (1974)

Annales de l'institut Fourier

Let R be a hyperbolic Riemann surface, d χ a harmonic measure supported on the Martin boundary of R , and H ( d χ ) the subalgebra of L ( d χ ) consisting of the boundary values of bounded analytic functions on R . This paper gives a complete classification of the closed H ( d χ ) -submodules of L p ( d χ ) , 1 p (weakly * closed, if p = , when R is regular and admits a sufficiently large family of bounded multiplicative analytic functions satisfying an approximation condition. It also gives, as a corollary, a corresponding result for the Hardy...

Invariant subspaces on open Riemann surfaces. II

Morisuke Hasumi (1976)

Annales de l'institut Fourier

We considerably improve our earlier results [Ann. Inst. Fourier, 24-4 (1974] concerning Cauchy-Read’s theorems, convergence of Green lines, and the structure of invariant subspaces for a class of hyperbolic Riemann surfaces.

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