Beurling's Theorem for the Bergman space

Das, Suman (2018) Beurling's Theorem for the Bergman space. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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It is interesting to study Hilbert spaces of analytic functions on the unit disk D and the operators on them. One of the most elementary of these operators is multiplication by the coordinate function z. The Hardy space H² constructs an important example in this area. A famous theorem by A. Beurling characterizes the invariant subspaces of H², and thus the invariant subspaces of the unilateral shift. In this thesis, we will be interested in the Bergman space L²a. It has been known for some time that the invariant subspace lattice of L2 a is very complicated when compared to that of H². In particular, not every invariant subspace of L²a is cyclic. Nevertheless, the following analogue of Beurling's Theorem is true and is the main result of this thesis: Theorem. Let M be an invariant subspace of L²a. Then: M = [M Ɵ zM]. Thus, as in the Hardy space case, invariant subspaces of L²a are in a one-to-one correspondence with their wandering subspaces.

Item Type: Thesis (Masters)
Additional Information: Supervisor: Dr. Subrata Shyam Roy
Uncontrolled Keywords: Bergman Space; Beurling's Theorem; Wandering Subspace Theorem
Subjects: Q Science > QA Mathematics
Divisions: Department of Mathematics and Statistics
Depositing User: IISER Kolkata Librarian
Date Deposited: 27 Nov 2018 05:36
Last Modified: 27 Nov 2018 05:37

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