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Best kernel approximation in Bergman spaces
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DOI：10.1016/j.amc.2021.126749.png)
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Abstract
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Let H be a reproducing kernel Hilbert space of analytic functions on the unit disk D. The best kernel approximation problem for His the following: given any positive integer n and any function f epsilon H find the best norm approximation of f by a linear combination of no more than n kernel functions K(z, z(k)), 1 <= k <= n. The purpose of this paper is to prove the existence of best kernel approximation for weighted Bergman spaces with standard weights. (C) 2021 Elsevier Inc. All rights reserved.
Keywords:
Bergman space
Reproducing kernel hilbert space
Blaschke product
Best kernel approximation
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