Interpolating sequences for the Bergman space.
نویسندگان
چکیده
منابع مشابه
General Interpolating Sequences for the Bergman Spaces
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these characterizations remain valid without that condition. The general interpolation we consider here includes the usual simple interpolation and multiple interpo...
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The author has previously shown that a sequence in the unit disk is a zero sequence for the Bergman space A if and only if a certain weighted L space contains a non-zero (equivalently, zero-free) analytic function. The weight in question is given by a simple formula summed over the zero set. Here we show that a sequence in the unit disk is an interpolating sequence for A if and only if it is se...
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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 characteriza...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1994
ISSN: 0026-2285
DOI: 10.1307/mmj/1029004915