Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan will hold its next weekly seminar on September 19, 2018, 10:00 a.m., which will feature a report by professor Bilal Bilalov, corresponding member of the NAS of Azerbaijan and the head of the Department of Non-Harmonic Analysis of IMM of the NAS of Azerbaijan, entitled “On basicity of the perturbed system of exponents in Morrey type spaces”.

In the report the perturbed system of exponents {e^{i(n-ßsignn)t}}_neZ is considered, where ß is a certain complex parameter. A necessary and sufficient condition is found  for the parameter ß, under which this system forms a basis in the Morrey space on the interval ( -π, π ). It should be noted that this system is of particular interest in the theory of nonharmonic Fourier series and its basis properties in Lebesgue spaces have been studied in the works of Paley-Wiener and Levinson. A basicity criterion of this system with respect to the parameter ß in Lebesgue spaces was obtained in the works of A.M. Sedletskii and E.I. Moiseev. We note that the basicity criterion in Morrey spaces differs from the criterion in Lebesgue spaces.

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