Chair of Higher Mathematics

The Chair of Higher Mathematics of the YSU Faculty of Physics was established in 1966 at the initiative of the dean of the faculty Ter-Mikayelyan. Until 1980, it was called the Chair of Mathematical Physics.

The Chair staff used to teach the following general and professional mathematical subjects at the Faculty of Physics and Radiophysics: mathematical analysis, analytic geometry, linear algebra, differential equations, integral equations, theory of functions of a complex variable, equations of mathematical physics, numerical methods, discrete mathematics, graph theory, probability theory, mathematical statistics, linear approximations, nonlinear approximations, functional analysis, real analysis, orthogonal polynomials, special functions, Fourier transforms, asymptotic methods, digital signal processing, etc.

From 1966 to 1979, the first head of the Higher Mathematics Chair was Ph.D., Professor Hanri Nersisyan, who is now an Academician of the National Academy of Sciences of the Republic of Armenia and works at the NAS Institute of Mathematics. In those years, under Nersisyan’s leadership, 3 graduates of the Faculty of Physics defended their doctoral theses in the specialty "Equations of Mathematical Physics", later becoming Ph.Ds.

The chair was also headed by Associate Professors Ferdinand Talalyan (1979-1986), Sargis Hakobyan (1986-1988), and Anatoli Kitbalyan (1989-2002).

Since 2003, the chair has been headed by Ph.D., Professor Martin Grigoryan.

In 2012, based on the research of the scientific group led by Grigoryan, the laboratory of linear and non-linear approximations and their application was established, where promising young scientists are also involved in the educational process as teachers.

In 2010, due to research dedicated to non-linear approximations ("Greedy" algorithm) Martin Grigoryan, the head of the chair, was granted the RA President's Award. Grigoryan has been included in the list of winners of highly effective researchers 4 times in a row ("Efficient Researcher Competition").

The research carried out at the Chair of Higher Mathematics is devoted to the problems of linear and nonlinear approximations with both classical and general orthonormal systems in different functional spaces, due to which important results have been obtained.

The chair staff has also:

• Solved many important problems concerning the convergence of the Fourier series. In particular, it was possible to rearrange the trigonometric system in such a way that the newly obtained one is in some sense better than the natural arrangement.

• Conducted research on fast Fourier models.

• Fixed many edge issues.

• Constructed a quasi-greedy basis in L1 space. All quasi-greedy subsystems of the Haar system in L1 space have been described.

• Described all the democratic subsystems of the Haar system. Similar results were obtained in the multivariate case.

• Derived new Littlewood - Paley inequalities for holomorphic and harmonic functions in complex and real multidimensional spaces, which solve a well-known Littlewood problem.

• Described mixed-norm weighted spaces in multidimensional domains, including by operations of fractional integration and differentiation operators. Such characterizations are made for Hardy, BMO, Bloch, Lipshitz, and Besov weight classes.

• Solved the problem of harmonic decomposition in Bergman's well-known classes within the framework of quaternion analysis. To this end, new maximum theorems were proved in Bergman's classes.

• Carried out scientific research dedicated to the existence and structure of universal functions for classical systems in recent years. Valuable results were obtained, which were published in high-ranking international mathematical journals. Let us mention 2 of them.

1. An integrable function was built, whose trigonometric system Fourier series is a universal series concerning symbols in functional spaces Lp[0,1), p∈(0,1). (each function of these spaces is represented by a co-linear series with the space metric obtained by changing the signs of some terms of the Fourier series of the constructed function).

2. It has been proved that almost everywhere, by changing the values of each finite measurable function on a small set, it is possible to obtain a universal function endowed with the mentioned property.

Similar results were also obtained for some classical systems, in particular, in the case of the Walsh system, it was possible to provide the norm of the Fourier series of universal functions and the convergence almost everywhere and the reduction of the modules of the Fourier coefficients.

Finally, one of the graduates of the Institute A. Minasyan founded a scientific and educational center in 2012, which has achieved considerable success in the field of information technologies. It is noteworthy that in one of its departments (KRISP) both senior students of the Institute of Physics and university graduates of different years such as programmers and researchers, physicists and mathematicians work.