The basis property of a perturbed system of exponentials in Morrey-type spaces

for the perturbed system of exponentials $\exp (i (n-\beta \operatorname{sign} n )t )$, for $n\in Z$, where $\beta$ is a complex parameter, we find a necessary and sufficient condition on $\beta$ under which this system constitutes a basis for the Morrey space on $(-\pi, \pi)$. 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 $\beta$ in Lebesgue spaces. The criterion for Morrey spaces is different from the above.