Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross
Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross
Department of Math & Statistics Technical Report Series
In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space Lpa(G), 1 < p < 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces Dq, q > 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on Lpa(𝔻), 1 < p < 2.
Invariant Subspaces Of Bergman Spaces On Slit Domains, William T. Ross
Invariant Subspaces Of Bergman Spaces On Slit Domains, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper, we characterize the z-invariant subspaces that lie between the Bergman spaces Ap(G) and Ap(G\K), where 1 < p < ∞, G is a bounded region in C, and K is a closed subset of a simple, compact, C1 arc.
Analytic Besov Spaces And Invariant Subspaces Of Bergman Spaces, William T. Ross
Analytic Besov Spaces And Invariant Subspaces Of Bergman Spaces, William T. Ross
Department of Math & Statistics Faculty Publications
In this paper, we examine the invariant subspaces (under the operator f -->z f) M of the Bergman space pa (G\T) (where 1 < p < 2, G is a bounded region in C containing D, T is the unit circle, and D is the unit disk) which contain the characteristic functions xD and xG, i.e. the constant functions on the components of G\T. We will show that such M are in one-to-one correspondence with the invariant subspaces of the analytic Besov space ABq (q is the conjugate index to p) and …