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Approximation of the Müntz-Szász type in weight spaces L p and zeroes of functions of Bergman classes in a half-plane

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Abstract

We study the completeness of the system of exponents exp(−λ n t), Re λ n > 0, in spaces L p with the power weight on the semiaxis ℝ+. We prove a sufficient condition for the completeness; one can treat it as a modification of the well-known Szász condition. With p = 2 it is unimprovable (in a sense). The proof is based on the results (which are also obtained in this paper) on the distribution of zeroes of functions of the Bergman classes in a half-plane.

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References

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Authors and Affiliations

  1. Moscow State University, Main Building, GSP-1 Vorob’yovy Gory, Moscow, 119991, Russia

    A. M. Sedletskii

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  1. A. M. Sedletskii
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Correspondence to A. M. Sedletskii.

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Dedicated to the memory of Petr Lavrent’evich Ul’yanov on the occasion of his 80th anniversary

Original Russian Text © A.M. Sedletskii, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 5, pp. 92–100.

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Sedletskii, A.M. Approximation of the Müntz-Szász type in weight spaces L p and zeroes of functions of Bergman classes in a half-plane. Russ Math. 52, 80–87 (2008). https://doi.org/10.3103/S1066369X08050101

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  • DOI: https://doi.org/10.3103/S1066369X08050101

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