Displaying similar documents to “Invariant subspaces on open Riemann surfaces. II”

Invariant subspaces on open Riemann surfaces

Morisuke Hasumi (1974)

Annales de l'institut Fourier

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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...