Department of Pure Mathematics

Founded in 2015

School of Mathematics and
Computer Sciences

V.N. Karazin Kharkiv
National University

Faculty

Vladimir . Dubovoy Full professor of the department of pure mathematics, doctor of sciences in mathematics

Sergey . Favorov Full professor of the department of pure mathematics, doctor of sciences in mathematics

Sergey . Gefter Associate professor of the department of pure mathematics, head of the department of pure mathematics, phd in mathematics

Vyacheslav . Gordevskyy Full professor of the department of pure mathematics, doctor of sciences in mathematics

Vladimir (Volodymyr) M. Kadets Full professor of the department of pure mathematics, doctor of sciences in mathematics

Mariya . Shcherbina Professor of the department of pure mathematics

Dmitry . Shepelsky Doctor of sciences in mathematics

Alexander L. Yampolsky Professor of the department of pure mathematics, doctor of sciences in mathematics

Dmytry V. Bolotov Doctor of sciences in mathematics

Vasyl O. Gorkavyy Doctor of sciences in mathematics, associate professor

Alexander V. Rezounenko Professor of the department of pure mathematics, doctor of sciences in mathematics

Anna M. Vishnyakova Professor of the department of pure mathematics, doctor of sciences in mathematics

Tamara . Fastovska Associate professor of the department of pure mathematics, phd in mathematics, associate professor

Nataliуa . Girya Associate professor of the department of pure mathematics, phd in mathematics

Oleksii . Hukalov Associate professor of the department of pure mathematics, phd in mathematics

Eugene . Karolinsky Associate professor of the department of pure mathematics, phd in mathematics

Eugene V. Petrov Phd in mathematics, senior lecturer

Aleksey . Shcherbina Phd in mathematics, senior lecturer

Olena O. Shugailo Phd in mathematics, senior lecturer

Viktoria V. Davydova Engineer

Iryna V. Kats Leading engineer

Thu Hien . Nguyen

Dmytro . Seliutin

Olesia O. Zavarzina Ph.d., senior lecturer

gefter@karazin.ua

Schedule

Sergey . Gefter

Associate professor of the department of pure mathematics, head of the department of pure mathematics, phd in mathematics

Link on external publications: google.scholar.

List of selected publications

Sergey Gefter, Aleksey Piven Entire solutions of one linear implicit differential-difference equation in Banach spaces // Ukrains’ kyi Matematychnyi Zhurnal, 2018, (70), #8, 1044-1057,

We establish the existence and uniqueness conditions for the solution for the initial problem in the classes of entire functions of exponential type. Closed linear operators act on Banach spaces and can be degenerate. We also present an example of application of abstract results to partial differential equations.

Sergey Gefter, Aleksey Piven Implicit linear difference equation in Frechet spaces // Dopov. Nac. akad. nauk Ukr. , 2017, 6:3-8,

An criterion of the existence and the uniqueness for a solution of the implicit linear difference equation Axn+1+Bxn=gn, where A and B are continuous operators, which act on Frechet spaces, is proved. Explicit formulas for the solution of this equation are found. For the case of Banach spaces, the results are specified.

Keywords: Frechet space, implicit difference equation

S. L. Gefter, A. L. Piven’ Initial problem for a nonhomogeneous linear differential-difference equation in a Banach space for a class of exponential type entire functions // European Journal of Mathematics, 2020. Vol. 6. P. 197-207,

We prove the existence and uniqueness of a solution to a one-point initial problem for the nonhomogeneous linear differential-difference equation u′(z)=Au(z+h)+f(z), z∈C, in some classes of exponential type entire vector-valued functions. The obtained formula for the unique solution can be considered as a generalization of the classical Cauchy formula for a solution to the nonhomogeneous linear differential equation.

S.L. Gefter, V. V. Martseniuk & A. L. Piven’ INTEGER SOLUTIONS OF A SECOND ORDER IMPLICIT LINEAR DIFFERENCE EQUATION // Bukovinian Mathematical Journal. , 6, 3-4 (Mar. 2019).,

We consider the following second order linear diﬀerence equation cx_{n+2}\;=\;bx_{n+1}+ax_n-f_n,\;n=0,1,2,... where a,b,c i f_n be integers (n = 0,1,2,...). If c = ±1 then we have the explicit equation and, obviously, for any initial data x0,x1 ∈ Z this equation has a unique integer solution. In what follows we assume c ≠ ±1 and b or a is not divisible by c. Under this assumption the equation is called implicit over the ring Z. If the equation is considered over some ﬁeld (for example, the ﬁeld of real numbers) then the concept of the implicit equation makes no sense. In this case the theory of linear diﬀerence equations is well developed. Recently the ﬁrst order implicit diﬀerence equations were studied over Z.

Keywords: LINEAR DIFFERENCE EQUATION