On the theory of finite groups

This is the author's abstract of his dissertation in the competition for the academic degree of Doctor in the Physico-Mathematical Sciences. The dissertation was defended on the 21st of January, 1969 at the Academic Council of the Institute of Mathematics of the Academy of Sciences of the USSR. The official opponents were: S. N. Chernikov, Corresponding Member, Academy of Sciences of the USSR and Professor B. I. Plotkin, Doctor of Physico-Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 347–360, September, 1969.     

Quasi-random dynamical systems

This paper is the author's abstract of his dissertation for the degree Doctor of Physiomathematical Science. The dissertation was defended on March 7, 1969, in the Study of the Soviet Mechanical-Mathematical Faculty of the M. V. Lomonosov Moscow State University. Official opponents: Academician A. N. Kolmogorov, Dr. of Physicomathematical Sciences D. V. Anosov, and Dr. of Physicomathematical Sciences Professor V. B. Lidskii.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 489–498, October, 1969.     

Direct and inverse approximation theorems in Banach spaces and Fourier transforms

An author's summary of a thesis submitted for the degree of Doctor of Physico-Mathematical Sciences. The dissertation was defended December 19, 1969, at a session of the scientific council of the Mechanical-Mathematics Faculty of the M. V. Lomonosov Moscow State University. The official opponents were Professors V. K. Dzyadyk, B. M. Levitan, and S. B. Stechkin, all Doctors of physico-mathematical sciences.Translated from Matematicheskie Zametki, Vol. 7, No. 6, pp. 765–778, June, 1970.     

General theory of statistical decisions

Author's abstract of the dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Physical-Mathematical Sciences. The dissertation was defended on January 21, 1969 at the Scientific Council of the Institute of Applied Mathematics of the Academy of Sciences of the SSSR. The official opponents of the thesis were: Academician Yu. V. Linnik, Corresponding Member of the Academy of Sciences SSSR A. A. Lyapunov, Academician of the Academy of Science USSR B. V. Gnedenko, and Doctor of Physical-Mathematical Sciences Professor F. I. Karpelovich.Translated from Matematicheskie Zametki, Vol. 5, No. 5, pp. 635–648, May, 1969.     

Resonance theorems and functional series

Self-referred dissertation in competition for the academic doctor's degree in physico-mathematical sciences (printed with elisions). The dissertation was defended on May 7, 1971 at the teaching council of the mechanics-mathematics faculty of the Moscow State University. The official opponents were: Dr. Physico-Mathematical Sciences, Prof. N. P. Kuptsov, Dr. Physico-Mathematical Sciences, Prof. A. M. Olevskii, and Corresponding Member of the Academy of Sciences of the Armenian SSR, Dr. Physico-Mathematical Sciences, Prof. A. A. Talalyan.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 583–595, November, 1971.The author extends hearty thanks to Prof. P. L. Ul'yanov for purposeful scientific conferences on the results of the dissertation.     

The theory of thermal potentials and its applications

A review by the author of his dissertation presented for the academic degree of doctor of physico-mathematical sciences. A defense of the dissertation was given on February 29, 1968 before the science committee of the V. A. Steklov Institute of Mathematics of the Academy of Sciences of the USSR. Official challengers were A. V. Bitsadze and A. A. Samarskii, Corresponding Members of the Academy of Sciences of the USSR, and V. P. Mikhailov, Doctor of Physico-Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 4, No.1, pp. 113–123, July, 1968.     

Spaces of kinematic type

The present paper is based on the author's dissertation for the degree of Doctor of Mathematical Physics. The dissertation was defended on November 27, 1969, at a meeting in the V. A. Steklov Institute of Soviet Mathematics, Academy of Sciences of the USSR. The official referees were Academician A. D. Aleksandrov, Doctor of Mathematical Physics, Professor Yu. F. Borisov, and Doctor of Mathematical Physics, Professor V. A. Efremovich.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 641–653, May, 1970.     

On conjugate functions and trigonometric series

The present paper is an abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Physical and Mathematical Sciences. The dissertation was defended on June 30, 1967 before the Academic Council of the Faculty of Mechanics and Mathematics of the M. V. Lomonosov Moscow State University. The official opponents were Professor A. V. Efimov, Doctor of Physical and Mathematical Sciences, Professor V. A. Il'in, Doctor of Physical and Mathematical Sciences, and Professor G. P. Tolstov, Doctor of Physical and Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 695–702, December, 1967.     

The multidimensional plateau problem in Riemannian varieties

This paper is the author's abstract of his dissertation for the degree of Doctor of Physico-Mathematical Sciences. The dissertation was defended on September 29, 1972 at a session of the Council of the Mechanico-Mathematical Faculty of M. V. Lomonosov Moscow University. The official opponents were Prof. V. M. Alekseev, Doctor of Phys.-Mat. Sci.; Prof. D. V. Anosov, Doctor of Phys.-Mat. Sci.; and Prof. M. M. Postnikov, Doctor of Phys.-Mat. Sci.Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 159–167, January, 1973.     

Partitions and centralizers in the theory of finite groups

This paper is the author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on February 10, 1969 at a united council for adjudicating academic degrees in mathematical sciences at the A. M. Gor'kii Urals State University. Official opponents: Corresponding Member of the Academy of Sciences of the USSR M. I. Kargapolov, Corresponding Member of the Academy of Sciences of the Ukrainian SSR S. N. Chernikov, Doctor of Physicomathematical Sciences Professor B. I. Plotkin, and Doctor of Physicomathematical Sciences V. S. Charin.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 499–511, October, 1969.     

Convolution equations in multidimensional spaces

Author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on Nov. 10, 1977, at the session of the Specialized Council D 002.38.03 at the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. Official opponents: Corresponding Member of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences, Professor A. G. Vitushkin; Corresponding Member of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences, Professor V. K. Ivanov; Doctor of Physicomathematical Sciences, Professor Yu. F. Korobeinik.Translated from Matematicheskie Zametki, Vol. 25, No. 5, pp. 761–774, May, 1979.     

Investigation of boundary value problems for elliptic systems of first order

This paper is the author's abstract of a dissertation submitted for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended November 2, 1972 at a session of the Scientific Council of the V. A. Steklov Mathematical Institute of the Academy of Sciences, USSR. Official referees: Corresponding Member of the Academy of Sciences of the USSR Professor A. V. Bitsadze, Corresponding Member of the Academy of Sciences of the USSR Professor M. M. Lavrent'ev, and Doctor of Physicomathematical Sciences, Professor P. I. Lizorkin.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 291–304, August, 1973.     

Isometric imbedding in E3 of noncompact domains of nonpositive curvature

Author's abstract of a dissertation for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended on Oct. 21, 1977, at a session of the Specialized Council D 002.38.02 at the V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. Official opponents: Academician of the Academy of Sciences of the USSR, Doctor of Physicomathematical Sciences A. V. Pogorelov; Professor, Doctor of Physicomathematical Sciences É. G. Poznyak; Professor, Doctor of Physicomathematical Sciences A. S. Fedenko.Translated from Matematicheskie Zametki, Vol. 25, No. 5, pp. 785–797, May, 1979.     

Conjugate functions

This is the author-review of a dissertation for the competition of the academic degree of Doctor of Physicomathematical Sciences (published with abbreviations). The dissertation was defended on June 30, 1976, in the academic council of the A. M. Razmadze Tbilisi Mathematics Institute of the Academy of Sciences of the Georgian SSR. The official opponents were: Professor N. N. Bakhaniya, Doctor of Physicomathematical Sciences; Professor Sh. S. Pkhakadze, Doctor of Physicomathematical Sciences; Professor A. A. Talalyan, Corresponding Member of the Academy of Sciences of the Armenian SSR and Doctor of Physicomathematical Sciences; and Professor S. A. Telyakovskii, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 771–783, November, 1977.     

On the theory of linear systems of ordinary differential equations

Author's abstract of dissertation for the attainment of the scientific degree of Doctor of the Physical and Mathematical Sciences. Dissertation defended May 24, 1968 at the sitting of the Council of the Mechanical and Mathematical Faculty of the M. V. Lomonosov State University.Official opponents: Doctor of the Physical and Mathematical Sciences D. V. Anosov, Doctor of the Physical and Mathematical Sciences Professor R. é Vinograd, and Doctor of the Physical and Mathematical Sciences Professor Ya. G. Sinai.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 483–490, October, 1968.     

Finite-dimensional perturbations of Volterra operators

This paper is a review by the author of his dissertation, presented in competition for the academic degree of Doctor of Physicomathematical Sciences. This dissertation was defended on December 20, 1973 at the Scientific Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. The examining committee consisted of Professor A. G. Kostyuchenko, Doctor of Physicomathematical Sciences; Professor A. F. Leont'ev, Corresponding Member of the Academy of Sciences of the USSR; and Professor M. K. Fage, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 669–680, October, 1974.     

Solvable subgroups of finite simple groups

This article is the author's abstract of his dissertation for the degree Doctor of Physico-mathematical Sciences. The dissertation was defended on September 17, 1973, at the session of the Academic Council on the conferring of academic degrees in the mathematical sciences of the Uralian Order of the Red Banner of Labor of the A. M. Gor'kii State University. The official opponents were: Professor A. I. Shirshov, Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences; Professor A. I. Kostrikin, Doctor of Physicomathematical Sciences; Professor A. I. Starostin, Doctor of Physicomathematical Sciences; Professor L. A. Shemetkov, Doctor of Physico-mathematical Sciences. The chief institution was the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR.Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 833–842, November, 1974.     

Infinite solvable and finitely approximable groups

Author's abstract of a dissertation presented as a requirement for the academic degree of Doctor of Physical and Mathematical Sciences. The dissertation was defended on June 21, 1974 at a meeting of the Academic Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. Official opponents: Professor Yu. L. Ershov, Professor S. I. Adyan, and Professor A. I. Starostin.     

On the existence of an optimal solution of the epsilon variational problem

It has been shown that known sufficient conditions for existence of optimal control imply existence of an optimal solution of the nondynamic epsilon variational problem as formulated by Balakrishnan.This work forms a part of the doctoral dissertation submitted by the author in early 1969 at UCLA and was supported in part by the Air Force Office of Scientific Research under Grant No. 69–1646. The author expresses his gratitude to Professor A. V. Balakrishnan for many useful discussions in the preparation of this work.     

Investigations of multidimensional,infinite-dimensional and limit theorems of the theory of probabilities

Author's abstract of a dissertation in competition for the scientific degree of Doctor of Physical-Mathematical Sciences. The dissertation was defended on May 30, 1968 at a meeting of the Scientific Council of the V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR. The official opponents were: V. S. Korolyuk, Corresponding Member, Academy of Sciences of the Ukrainian SSR, A. V. Skorokhod, Corresponding Member, Academy of Sciences of the Ukrainian SSR, and V. A. Statulyavichus, Doctor of Physical-Mathematical Sciences.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 611–619, November, 1968.