Geodesic
Invariant Subspaces on Riemann Surfaces
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 399-403

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we generalize to Riemann surfaces a theorem of Helson and Lowdenslager in (2) describing the closed subspaces of L 2({|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 L 2(Γ, dμ) that are invariant under multiplication by functions in A (R) = {F|F continuous on , analytic on R}. 
Voichick, Michael. Invariant Subspaces on Riemann Surfaces. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 399-403. doi: 10.4153/CJM-1966-042-8
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[1] 1. Hasumi, M., Invariant subspaces for finite Riemann spaces (ditto copy, 1964). Google Scholar

[2] 2. Helson, H. and Lowdenslager, D., Invariant subspaces, Proc. Intern. Symposium on Linear Spaces, Jerusalem (New York, 1961), pp. 251–262. Google Scholar

[3] 3. Hoffman, K., Banach spaces of analytic functions (Englewood Cliffs, N.J., 1962). Google Scholar

[4] 4. Pfluger, A., Theorie der Riemannschen Flächen (Berlin-Gottingen-Heidelberg, 1957). Google Scholar

[5] 5. Royden, H. L., The boundary values of analytic and harmonic functions, Math. Z., 78 (1962), 1–24. Google Scholar

[6] 6. Sarason, D., The Hp spaces of annuli (Dissertation, University of Michigan, 1963). Google Scholar

[7] 7. Sarason, D., Doubly invariant subspaces of annulus operators, Bull. Amer. Math. Soc., 69(1963), 593–596. Google Scholar

[8] 8. Voichick, M., Ideals and invariant subspaces of analytic functions, Trans. Amer. Math. Soc, 111 (1964), 493–512. Google Scholar

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