Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-16T00:53:10.711Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bishop, E., A general Rudin-Carlson theorem, Proc. Amer. Math. Soc, 13 (1962), 140–143.Google Scholar
2. Hasumi, M. and Srinivasan, T. P., Invariant subspaces of continuous functions, Can. J. Math., 17 (1965), 643–651.Google Scholar
3. Royden, H. L., The boundary values of analytic and harmonic functions, Math. Z., 78 (1962), 1–24.Google Scholar
4. Sarason, D., Doubly invariant subspaces of annulus operators, Bull. Amer. Math. Soc, 69 (1963), 593–596.Google Scholar
5. Schiffer, M. M. and Spencer, D. C., Functionals of finite Riemann surfaces (Princeton, 1954).Google Scholar
6. Srinivasan, T. P., Doubly invariant subspaces, Pacific J. Math., 14 (1964), 701–707.Google Scholar
7. Srinivasan, T. P., Simply invariant subspaces and generalized analytic functions, Proc. Amer. Math. Soc., 16 (1965), 813–818.Google Scholar
8. Voichick, M., Ideals and invariant subspaces of analytic functions, Thesis, Brown University, 1962.Google Scholar
9. Wermer, J., Subalgebras of the algebra of all complex-valued continuous functions on the circle, Amer. J. Math., 78 (1956), 225–242.Google Scholar