Classes of functions and Fourier coefficients with respect to complete orthonormal systems

This is the author review of a dissertation presented in the competition for the academic degree of Doctor of Physicomathematical Sciences. The dissertation was defended on October 10, 1974 in a meeting of the academic council of the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. The official opponents were: A. A. Talalyan, Corresponding Member of the Academy of Sciences of the Armenian SSR; N. P. Kuptsov, Doctor of Physicomathematical Sciences; and E. M. Nikishin, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 445–463, September, 1976.     

Series with respect to the Schauder system

Unconditional convergence in the C(0, 1) metric and convergence almost everywhere of series with respect to the Schauder system are investigated.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 453–460, October, 1968.     

Mass-spectrometric study of the cleavage products of 3,4-epoxytetrahydropyrans by amines

Conclusions Only 4-methyl-3-amino-4-hydroxytetrahydropyrans are formed when the oxide ring of 4-methyl-3,4-epoxytetrahydropyran is opened by ammonia and amines. The structural isomers of 4-amino-3-hydroxy-and 3-amino-4-hydroxytetrahydropyran are formed in the analogous reaction of the unsubstituted 3,4-epoxy-tetrahydropyran, the mutual arrangement of the substituents in which was determined on the basis of analyzing the mass spectra.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 636–639, March, 1971.     

Terbium-containing copolymers based on the norbornene functional derivatives. Synthesis, photoluminescent and electroluminescent properties

New carbazole- and terpyridine- containing norbornene derivatives were synthesized and structurally characterized. On the basis of these compounds by the method of metathesis polymerization copolymers were obtained with carbazole and terpyridine fragments in side chains. The synthesized copolymers react with terbium pyrazolonate complex to form the terbium-containing polymeric materials exhibiting the metalcentered photo- and electroluminescence.     

Complex of copper(I) with norbornene-substituted pyridinylbenzimidazole ligand and copper-containing carbochain copolymers based on this complex: Synthesis, photo- and electroluminescent properties

New complex of copper(I) with norbornene-substituted 1-H-2-pyridinylbenzimidazole ligand was synthesized. The compound obtained enters into a metathesis polymerization reaction to give carbochain coppercontaining copolymers exhibiting photo-and electroluminescent properties.     

On the theory of nonlinear Thomson scattering of a highly focused laser pulse

The problem of nonlinear Thomson scattering of an ultrashort laser pulse on free electrons from a sharp focus is solved within the test particle approach. To describe the laser beam fields, an exact solution to the Helmholtz equation is used, which allows simulation of the electron dynamics and emission when the paraxial approximation is certainly inapplicable. Characteristics of attosecond electromagnetic pulses of secondary emission from test electrons during their motion near the laser focus are studied.