Today the institute seminar of IMM was held. At the seminar the head of “Nonharmonic Analysis” department, the corr. member of ANAS, prof. B. Bilalob made a report on “Basicity of the perturbed system of exponenets in Morrey type spaces”.

In the report the perturbed exponent system {e^{i(n-ßsignn)t}}_neZ was considered in the case when ß is a certain complex parameter. Necessary and sufficient conditions on ß parameter were found. Under certain conditions this system makes a basis in Morrey type space in the interval ( -π, π ).

This type system is of special interest in theory of nonharmonic Fourier series. Its basicity properties in Lebesgue systems were studied in Paley-Wiener and Levinson’s works.

The basicity criterion of this system with respect to ß parameter was obtained in Lebesgue spaces in A.M. Sedletsky and E.I. Moiseev’s works.

It should be noted that the basicity criterion in Morrey spaces differ from basicity criterion in Lebesgue spaces.

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