Russian

During the period from September 28 to 30, 2026 the online workshop on operator theory in function spaces and its applications dedicated to the 85-th anniversary and the 60th anniversary of the scientific and pedagogical activity of the famous Russian mathematician, Professor of the Institute of Mathematics of Peoples' Friendship University of Russia, Doctor of Sciences, Professor Victor I. Burenkov, D.Sc. will be held. For more details about the jubilarian, see below.

Organizers

The Workshop is organized by:

  • Vladikavkaz Scientific Center of the RAS (Southern Mathematical Institute; North-Caucasus Center for Mathematical Research*) (SMI VSC RAS; NCCMR VSC RAS). 
  • Lomonosov Moscow State University (Faculty of Mechanics and Mathematics, Department of General Control Problems) (MSU); 
  • Peoples' Friendship University of Russia named after Patrice Lumumba (Institute of Mathematics of Peoples' Friendship University of Russia) (MI RUDN University).

*Workshop is supported by the Ministry of Science and Higher Education of Russian Federation, project № 075-02-2026-738.

Organizing Committee

Co-chairs of the Organizing Committee: 

  • Prof. Anatoly G. Kusraev (VSC RAS; Vladikavkaz, Russia); 
  • Prof. Georgy G. Magaril-Il’yaev (MSU; Moscow, Russia); 
  • Prof. Andrey B. Muravnik (MI RUDN University; Moscow, Russia). 

Executive Team: 

  • PhD Student Alina A. Saadulaeva (SMI VSC RAS; Vladikavkaz, Russia) – the secretary; 
  • Junior Researcher Victoria A. Tamaeva (SMI VSC RAS; Vladikavkaz, Russia); 
  • PhD Batradz B. Tasoev (SMI VSC RAS; Vladikavkaz, Russia). 

Workshop Details

The work will be held online from September 28 till 30, 2026. To participate the Workshop and receive a link to connect to the Workshop sessions, it is necessary to fill in the registration form located at the link. 

The registration deadline is September 26, 2026. 

All the registered participants will receive the connection link as well as the Workshop program till September 27, 2026 (inclusive). 

The languages of the Workshop are English and Russian. 

Workshop Program

The Workshop program  will be sent to all registered participants  no later than September 27, 2026 (inclusive). 

Workshop Program

About the hero of the day

Victor Ivanovich Burenkov made a remarkable contribution to modern mathematical science. In the works of Victor Ivanovich, the theory of functions, functional analysis, and the theory of differential operators got significant development; fundamental problems of the theory of function spaces and the spectral theory of elliptic operators were solved.

Burenkov's theorem on the superposition of absolutely continuous functions, stating that the superposition of absolutely continuous functions multiplied be the absolutely continuous derivative is absolutely continuous (while the superposition of absolutely continuous functions itself may be not absolutely continuous) got the approval of the famous Academician A. N. Kolmogorov. Also there are well known  results of Kolmogorov type on exact constants in inequalities for norms of derivatives, obtained in a number of joint works by V. I. Burenkov and V. A. Gusakov, including the Burenkov-Gusakov theorem on exact constants in the Sobolev embedding theorems for the case of the Sobolev spaces defined on the cube.

Victor Burenkov developed the method of averaging operators with variable step and variable shift, with the help of which a number of theorems on the approximation of functions belonging to the Sobolev spaces and more general spaces by infinitely continuously differentiable  functions for arbitrary open sets were proved. On the basis of this method, Burenkov’s extension operator of was constructed for functions of the Sobolev spaces, enabling to extend them, in a certain sense optimal way, to the whole Euclidean space  with preservation of their differential properties from domains of definition with a Lipschitz boundary.

Together with A. L. Gorbunov, exact two-sided estimates of the minimal norm of such extension operators were obtained. Victor Ivanovich also posed and solved the problem of extending functions from the Sobolev spaces with the minimal deterioration of differential properties for irregular domains of definition.

V. I. Burenkov, jointly with Professor M. L. Gol'dman, proved that in the limiting case of the trace theorem on an m-dimensional subspace for the anisotropic Nikol'skii-Besov spaces defined on an n-dimensional Euclidean space (m<n), there exist only nonlinear extension operators from an m-dimensional subspace while in all non-limiting cases linear extension operators exist.

Together with M. Sh. Tuyakbaev (Kazakhstan), the problem of describing the space of multipliers of the Fourier integral in the weighted Lebesgue spaces with an exponential weight was studied. For this, it was required to use the Gevrey spaces. Necessary and sufficient conditions have been  found on the numerical parameters characterizing the Gevrey spaces under which they are embedded in the above-mentioned space of multipliers.

All these results are of enduring significance for the theory of functions and functional analysis.

V. I. Burenkov found necessary and sufficient conditions for the conditional hypoellipticity of differential operators. This fundamental result is now known as Burenkov's theorem on conditional hypoellipticity, and this type of hypoellipticity itself is rightfully called hypoellipticity according to Burenkov. Professor H. G. Ghazaryan (Armenia) continued research in this direction and obtained a number of interesting results.

In the field of spectral theory of differential operators, V. I. Burenkov has a number of joint publications with Professors E. B. Davies (Great Britain), P. D. Lamberti (Italy), and M. Lanza de Cristoforis (Italy) on the spectral stability of uniformly elliptic differential operators under the variation of the domain of definition and corresponding estimates for the deviation of eigenvalues. V.I. Burenkov, together with Professor P.D. Lamberti, developed a method cited as the Burenkov-Lamberti method of transition operators, which made it possible to reduce the problem of spectral stability to the problem of constructing the so-called transition operators and, with its help, to obtain exact estimates of the deviation of eigenvalues generated by the perturbation of domains of definition for a wide class of linear  elliptic differential operators and various homogeneous boundary conditions (1st, 2nd, and 3rd boundary value problems) through geometric characteristics of the proximity of domains of definition. The case of the nonlinear p-Laplacian was also considered.

In the last two decades, V. I. Burenkov has paid great attention to the study of Morrey-type function spaces and their applications. In 2003, he was the first to introduce into consideration general local Morrey-type spaces, which allowed him, together with Professor E. D. Nursultanov (Kazakhstan), to prove the closedness of the scale of such spaces with respect to the real interpolation method (it should be noted that the scale of the classical Morrey spaces is not closed with respect to the real interpolation method), as well as, together with a number of co-authors, to find necessary and sufficient conditions on the functional parameters of these spaces ensuring the boundedness in these spaces of a wide class of operators of real analysis. His main co-author on this topic is Corresponding Member of the National Academy of Sciences of Azerbaijan, Professor V. S. Guliyev. The Burenkov-Tararykova inequality for convolutions of functions for general Morrey-type spaces is expected to have numerous applications (this is a distant analogue of the classical Young inequality for convolutions of functions for the Lebesgue spaces, significantly different from it in formulation).

Taking into account the significant advances in the operator theory on Morrey-type spaces, stemming from the study of general local Morrey-type spaces, and the contribution of V.I. Burenkov to this theory, there is an opinion that it would be appropriate to henceforth designate this class of spaces as the Morrey-Burenkov spaces.

The results of V.I. Burenkov's research have been published in more than 190 scientific articles in leading mathematical journals. He has over 60 co-authors from more than 25 countries of the world, he has given over 100 plenary talks at authoritative conferences, and has also delivered lecture courses by invitation of leading universities in more than 30 countries of the world.

A significant place in the activity of V.I. Burenkov is occupied by scientific-pedagogical and organizational work.

In 2010, he was one of the initiators, together with Academicians of the National Academy of Sciences of Kazakhstan R. Oinarov and B. Zh. Abdraimov, then Rector of the L. N. Gumilyov Eurasian National University (ENU), of the creation of the international journal "Eurasian Mathematical Journal (EMJ)", published at the ENU, and since then for over 15 years he has been its Editor-in-Chief, together with Academician of the National Academy of Sciences of Kazakhstan M. Otelbaev and Rector of M.V. Lomonosov Moscow State University Academician of the Russian Academy of Sciences V.A. Sadovnichy. In 2018, the EMJ was assigned the category Q2 in the international Scopus database, in 2023 it received the Scopus Award Kazakhstan for significant contribution to world-class scientific research, and in 2024 the EMJ was assigned the highest category Q1 in the international databases Web of Science and Scopus.

Importantly, in the EMJ, papers that have received positive reviews from referees undergo thorough editing for the English language (free of charge). V.I. Burenkov’s wife, Tamara Vasilievna Tararykova, one of the Deputy Editors-in-Chief of the EMJ, and Ainur Maralkysy Temirkhanova, Managing Editor of the EMJ provided invaluable assistance to Victor Ivanovich in the work of editing the EMJ.

V.I. Burenkov is an honorary Professor/Doctor of Sciences of several universities and institutes in Russia and abroad (in Azerbaijan, Armenia, Czech Republic, Great Britain, India, Italy, Iran, Kazakhstan, Kyrgyzstan, Turkey).

In 2021, in recognition of his long standing fruitful joint research with Kazakhstani mathematicians and with successful work on the EMJ, V.I. Burenkov was elected a Foreign Member of the National Academy of Sciences of Kazakhstan, and, in 2026, he was awarded the ENU Medal for his contribution to the fields of science and education.

In 2017, V.I. Burenkov was at the origins of the creation of the Mathematical Institute named after Academician S.M. Nikol’skii at the Peoples' Friendship University of Russia named after Patrice Lumumba and served as its first director, laying a solid foundation for its scientific and pedagogical activities.

V.I. Burenkov is the author of a fundamental monograph on the theory of the Sobolev spaces "Sobolev Spaces on Domains", published in 1998 in Germany by the publishing house "Teubner-Texte zur Mathematik".  It became a widely sought-after book both for specialists in the theory of function spaces and for a broad range of mathematicians interested in applications of the theory of the Sobolev spaces. In Russia and a number of foreign countries it is used in universities as the main textbook on the theory of function spaces.

He is also the author of many textbooks for mathematics students and was the supervisor of over 25 defended Candidate of Sciences/PhD theses.

For 60 years of scientific and teaching activity, Victor Ivanovich Burenkov worked 40 years in Russian universities (1966-1968, Moscow Institute of Physics and Technology; 1968-1981, Moscow Institute of Radio Engineering, Electronics and Automation; 1981-1994 and 2014-2026, Peoples' Friendship University of Russia named after Patrice Lumumba) and 20 years in foreign universities (1994-2008, University of Wales, Cardiff, UK; 2006-2011, University of Padova, Padua, Italy;  2010-2014,   L.N. Gumilyov Eurasian National University , Astana, Kazakhstan).

V. I. Burenkov’s development as a professional mathematician was significantly influenced by Academician S. M. Nikol’skii (his doctoral advisor, scientific advisor during preparation for the defense of DSci thesis), Corresponding Member of the Russian Academy of Sciences (RAS) O. V. Besov (long-time head of the S. M. Nikol’skii Seminar on the Theory of Differentiable Functions of Several Variables at the Steklov Mathematical Institute of the RAS), and Corresponding Member of the RAS L. D. Kudryavtsev, under whom Burenkov took a two-year course on mathematical analysis at the Moscow Institute of Physics and Technology. He was also influenced by renowned scientists and lecturers in various fields of theoretical and applied mathematics and mechanics: A. A. Abramov, F. R. Gantmakher, A. A. Dezin, A. A. Dorodnitsyn, V. B. Lidskii, N. N. Moiseev. M. A. Naimark, and G. E. Shilov.

V. I. Burenkov has extensive experience of many years of mathematical communication, especially close with professors (in alphabetical order) A. V. Arutyunov, A. G. Aslanyan, E. I. Berezhnoi, S. K. Vodopyanov, M. L. Goldman, V. M. Goldstein, G. G. Magaril-Ilyaev, M. S. Nikolsky, A. P. Soldatov, A. Senouci, V. D. Stepanov, A. A. Shkalikov, with whom he has long been on a first-name basis (some of them are also his co-authors). Many of V. I. Burenkov’s colleagues know that he is also a “professional amateur” in sports (basketball, football, volleyball, skis, tennis, table tennis, chess) and took part in joint sports events with him.

Contacts