PRELIMINARY VERSION Interpolating Sequences for the Multipliers of the Dirichlet Space
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چکیده
The Dirichlet space D consists of all analytic functions f defined on the unit disk with ∫ |f (z)|dA < ∞. The space of multipliersMD consists of analytic functions φ with φf ∈ D for all f ∈ D. A sequence {zn} ⊂ is called an interpolating sequence for MD if for each bounded sequence of complex numbers {wn} there exists φ ∈ MD with φ(zn) = wn for all n. Our main result is a geometric characterization of the interpolating sequences for MD, answering a question of S. Axler. The first author is supported in part by NSF grant DMS-9302823. 1 §
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تاریخ انتشار 2004