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H2-Norms of Partial Sums of the Fourier Series in the Laguerre Basis for Bounded Holomorphic Functions

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Ukrainian Mathematical Journal Aims and scope

We compute the upper bounds for the H2-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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    V. V. Savchuk

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  1. V. V. Savchuk
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Correspondence to V. V. Savchuk.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 1, pp. 128–137, January, 2021. Ukrainian DOI: 10.37863/umzh.v73i1.2371.

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Savchuk, V.V. H2-Norms of Partial Sums of the Fourier Series in the Laguerre Basis for Bounded Holomorphic Functions. Ukr Math J 73, 144–155 (2021). https://doi.org/10.1007/s11253-021-01914-1

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  • DOI: https://doi.org/10.1007/s11253-021-01914-1

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