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A method of constructing conditional bases of power functions in certain Banach spaces of analytic functions

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Abstract

In this note, a, method of constructing conditional exponential bases in some Banach spaces of analytic functions is presented. The method of constructing basic families due to Figà-Talamanca is generalized. Concrete applications and examples of conditional basic families in the space of multipliers of power series with the sequence of Taylor coefficients from lp, in the space of multipliers of Cauchy-type integrals, and in other spaces are given. Bibliography: 12 titles.

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Authors
  1. A. N. Petrov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 170–199.

Translated by S. V. Kislyakov.

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Petrov, A.N. A method of constructing conditional bases of power functions in certain Banach spaces of analytic functions. J Math Sci 101, 3149–3165 (2000). https://doi.org/10.1007/BF02673740

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  • DOI: https://doi.org/10.1007/BF02673740

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