Abstract
We consider some properties of the reproducing kernels for Hilbert spaces of functions analytic in the unit disk; these preperties are related to double power series expansions. It turns out that some structure properties of the matrices of coefficients of these expanisons are determined by certain quadratic inequalities involving the operator of multiplication by an independent variable. As examples, we consider Dirichlet type spaces and weighted Bergman spaces.
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Shimorin, S. (2000). Double Power Series and Reproducing Kernels. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_27
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DOI: https://doi.org/10.1007/978-3-0348-8378-8_27
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9541-5
Online ISBN: 978-3-0348-8378-8
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