Professor of the Tula State University (2007–2023)

E-mail:

Website:

Education:

M. Sc. summa cum laude in Applied Mathematics, 1995, Tula State University, Tula.

Scientific biography:

→ 1999 – Ph. D. in Mathematics, "Uniform approximation of continuous functions of several variables" (Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow).

→ 2006 – D. Sc. in Mathematics, "Extremal problems in the theory functions and approximation theory and applications" (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg).

Research activity:

The participant of scholarships by RFBR, Ministry of Education and Science of the Russian Federation, RSCF, scientific programs of Krasovskii Institute of Mathematics and Mechanics (Yekaterinburg), Samara National Research University, Beijing Normal University and Tianjin Normal University (China), CRM Centre for Mathematical Research (Barcelona, Spain), Oberwolfach Research Institute for Mathematics (Germany), Isaak Newton Institute for Mathematical Sciences (Cambridge, UK), member of the editorial board of the journal "Analysis Mathematica" (Hungarian Academy of Sciences).

Research Interests:

Theory of approximation and classical inequalities, harmonic analysis and theory of functions, extremal problems for the classes of function of one or several variables, analytical methods of discrete geometry.

Keywords: theory of approximation, harmonic analysis, extremal problems, Fourier inequalities.

Teaching: he has trained three Doctors of Philosophy.

Honors and Awards:

→ The prize winner of the VIII Award of the Academia Europaea for young Russian scientists in Mathematics (2001).

→ Golden RAS Medal for Russian students in mathematics (2002).

→ Awarded by the administration of the Tula Region for achievements in scientific and educational work (2010).

Hobby: foreign languages.

Publications (recent, main):

→ L. De Carli, D. Gorbachev, S. Tikhonov, "Pitt inequalities and restriction theorems for the Fourier transform", Revista Matematica Iberoamericana, 33:3 (2017), 789–808, DOI.

→ D.V. Gorbachev, S.Y. Tikhonov, "Wiener's problem for positive definite functions", Mathematische Zeitschrift, 289:(3–4) (2018), 859–874, DOI.

→ D. Gorbachev, E. Liflyand, S. Tikhonov, "Weighted norm inequalities for integral transforms", Indiana Univ. Math. J. 67 (2018), 1949–2003, DOI.

→ D.V. Gorbachev, V.I. Ivanov, "Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem", Sb. Math., 210:6 (2019), 809–835 DOI.

→ D.V. Gorbachev, V.I. Ivanov, S.Yu. Tikhonov, "Positive \(L^p\)-bounded Dunkl- type generalized translation operator and its applications", Constructive Approximation, 49:3 (2019), 555–605, DOI.

→ D. Gorbachev, S. Tikhonov, "Doubling condition at the origin for non-negative positive definite functions", Proceedings of the American Mathematical Society, 147 (2019), 609–618, DOI.

→ L. De Carli, D. Gorbachev, S. Tikhonov, "Weighted gradient inequalities and unique continuation problems", Calculus of Variations and Partial Differential Equations. 59:3, art. 89, (2020), DOI.

→ F. Dai, D. Gorbachev, S. Tikhonov, "Nikolskii constants for polynomials on the unit sphere", Journal d'Analyse Mathematique, 140:1 (2020), 161–185, DOI.

→ D.V. Gorbachev, V.I. Ivanov, S.Yu. Tikhonov, "Sharp approximation theorems and Fourier inequalities in the Dunkl setting", Journal of Approximation Theory, 258 (2020), 105462, DOI.

→ D. Gorbachev, V. Ivanov, S. Tikhonov, "Uncertainty Principles for Eventually Constant Sign Bandlimited Functions", SIAM Journal on Mathematical Analysis, 52:5 (2020), 4751–4782, DOI.

→ D.V. Gorbachev, I.A. Martyanov, "Bounds of the Nikol'skii polynomial constants in \(L^p\) with Gegenbauer weight", Trudy Instituta Matematiki i Mekhaniki UrO RAN, 26:4 (2020), 126–137, DOI.

→ D.V. Gorbachev, V.I. Ivanov, S.Yu Tikhonov, "Riesz Potential and Maximal Function for Dunkl transform", Potential Analysis, 55 (2021), 513–538, DOI.

→ F. Dai, D. Gorbachev, S. Tikhonov, "Estimates of the asymptotic Nikolskii constants for spherical polynomials", Journal of Complexity, 2021, 101553, DOI.

→ D.V. Gorbachev, "Bernstein Inequality in \(L^p\) on the Line with Power Weight for \(p \gt 0\)", Math. Notes, 111:2 (2022), 308–311, DOI.

→ D.V. Gorbachev, V.I. Ivanov, "Logan–Hermite Extremal Problems for Entire Functions of Exponential Type", Math. Notes, 113:1 (2023), 143–148, DOI.