Abstract
AbstractWe consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A
Highlights
Let D denote the unit disk in the complex plane
−1 < α < ∞, the weighted Bergman space A2α is the space of holomorphic functions f in D such that
The space A2α is a Hilbert space with the inner product f, g α inherited from L2(D, dAα)
Summary
−1 < α < ∞, the weighted Bergman space A2α is the space of holomorphic functions f in D such that. Following [4], we define the space H(T ) to be the range of the operator (I − T T ∗)1/2 with the inner product given by (I − T T ∗)1/2f, (I − T T ∗)1/2g. Zhu proved that if φ is a finite Blaschke product B, as sets, H0(B) = H0(B) = H2, the Hardy space on the unit disk. These results were extended to positive α in [5], where the author proved that. We define the space D(α) to be the set of holomorphic functions in D and such that f ∈ L2(D, dAα).
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