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

Abstract

for the perturbed system of exponentials exp(i(n − β sign n)t), for n ∈ Z, 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.