NORMS OF PARTIAL SUMS OF THE FOURIER SERIES IN THE LAGUERRE BASIS FOR BOUNDED HOLOMORPHIC FUNCTIONS

NORMS OF PARTIAL SUMS OF THE FOURIER SERIES IN THE LAGUERRE BASIS FOR BOUNDED HOLOMORPHIC FUNCTIONS

We compute the upper bounds for the [H.sup.2]-norms of partial sums of the Fourier series in the Laguerre basis on the unit ball in the space of bounded holomorphic functions on unit disk. We present an application of the main result to the solution of some extreme problems in the theory of approxim...

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Veröffentlicht in:Ukrainian mathematical journal 2021-06, Vol.73 (1), p.144
1. Verfasser: Savchuk, V.V
Format: Artikel
Sprache:eng
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Zusammenfassung:We compute the upper bounds for the [H.sup.2]-norms of partial sums of the Fourier series in the Laguerre basis on the unit ball in the space of bounded holomorphic functions on unit disk. We present an application of the main result to the solution of some extreme problems in the theory of approximation of holomorphic functions.
ISSN:0041-5995
DOI:10.1007/s11253-021-01914-1