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


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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.

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B. Bilalov

Institute of Mathematics and Mechanics

编辑信件的主要联系方式.
Email: b_bilalov@mail.ru
阿塞拜疆, Baku

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