As the joint seminar of “Nonharmonic Analysis”, “Functional Analysis” and “Function Theory”, the doctor dissertation work in mathematics on “Some issues of basis theory and bases in generalized Lebesgue spaces of cand. of phys. Math. Sci. ass prof. Togrul Rafael oglu Muradov by specialty 12 02 01 analysis and functional Analysis was initially discussed. The dissertation work was devoted to basicity problems in generalized Lebesgue and Sobolev spaces.
The system of exponents with piecewise continuous space was considered and the basicity of the system in in variable exponent Lebesgue spaces was proved within certain conditions, Basicity of operator coefficient double system in Banach spaces was considered, relations between basicity of these systems was constructed, necessary conditions for basicity were obtained. The obtained results were applied to specific examples.
Mixed problems of variable exponent Lebegue spaces were considered in a special case, continuous analogue of classic Paley-Wiener theorem on Riesz basicity of the system of perturbed exponents was given. A method for basicity of perturbed systems of simes and cosines was offered. Sufficient condition for basicity of the perturbed system of cosines in variable exponent Sobolev space was given. The obtained results were applied to the basicity of the system consisting of the solutions of Cauchy problem for Strum-Liouville equation in generalized Lebesgue space. Togrul Rafael oglu Muradov has authored 40 scientific works , 21 papers including 12 papers abroad (four of them in Thomson Reuter journals) , 1 monograph (Germany), two textbooks (Russia) (Ukrainskii Matematicheskiy Zhurnal, estest I tekhn. nauki, Doklady RAN, International Journal of mathematical Analysis, etc. )

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