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Siberian Mathematical Journal

, Volume 60, Issue 2, pp 249–271 | Cite as

The Basis Property of a Perturbed System of Exponentials in Morrey-Type Spaces

  • B. T. BilalovEmail author
Article
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Abstract

for the perturbed system of exponentials exp(i(nβ sign n)t), for nZ, where β is a complex parameter, we find a necessary and sufficient condition on β under which this system constitutes a basis for the Morrey space on (−π, π). The system is of particular interest in the theory of nonharmonic Fourier series; the study of its basis property in Lebesgue spaces stems from the works by Paley, Wiener, and Levinson. Sedletskii and Moiseev obtained a criterion for the basis property for this system with respect to β in Lebesgue spaces. The criterion for Morrey spaces is different from the above.

Keywords

perturbed system of exponentials basis property Morrey space 

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsBakuAzerbaijan

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