Approximation theory and classical inequalities, harmonic analysis and function theory, extremal problems in one and several variables, analytical methods of metric geometry.
Biography
D. Sc. in Mathematics, November 2006, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, “Extremal problems in the theory functions and approximation theory and applications”.
Ph. D. in Mathematics, January 1999, Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, “Uniform approximation of continuous functions of several variables”.
M. Sc. summa cum laude in Applied Mathematics, July 1995, Tula State University, Tula.
Main publications:
D. Gorbachev, V. Ivanov, S. Tikhonov, “Uncertainty principles for eventually constant sign bandlimited functions”, DOI: 10.1137/20M131566X, SIAM J. Math. Anal., 52:5 (2020), 4751–4782
F. Dai, D. Gorbachev, S. Tikhonov, “Nikolskii constants for polynomials on the unit sphere”, DOI: 10.1007/s11854-020-0084-9, J. dAnal. Math., 140:1 (2020), 161–185
L. De Carli, D. Gorbachev, S. Tikhonov, “Pitt inequalities and restriction theorems for the Fourier transform”, DOI: 10.4171/RMI/955, Revista Matematica Iberoamericana, 33:3 (2017), 789–808
D. V. Gorbachev, “Extremum problem for periodic functions supported in a ball”, DOI: 10.4213/mzm508, Math. Notes, 69:3 (2001), 313–319
D. V. Gorbachev, “Extremal problem for entire functions of exponential spherical type, connected with the Levenshtein bound on the sphere packing density in $\mathbb{R}^{n}$”, Izvestiya of the Tula State University Ser. Mathematics, 6:1 (2000), 71–78
D. V. Gorbachev, “Multidimensional weighted inequalities for entire functions of exponential type”, Mat. Zametki, 116:5 (2024), 809–813; Math. Notes, 116:5 (2024), 1144–1148
2.
D. V. Gorbachev, A. P. Solodov, “New conditions for the convergence of a weak greedy algorithm”, Math. Notes, 116:3 (2024), 566–570
2023
3.
D. V. Gorbachev, “Boas conjecture on the axis for the Fourier–Dunkl transform and its generalization”, Chebyshevskii Sb., 24:2 (2023), 141–153
4.
D. V. Gorbachev, V. I. Ivanov, “Logan–Hermite Extremal Problems for Entire Functions of Exponential Type”, Mat. Zametki, 113:1 (2023), 138–143; Math. Notes, 113:1 (2023), 143–148
2022
5.
D. V. Gorbachev, N. N. Dobrovol'skii, “Some results for weighted Bernstein–Nikol'skii constants”, Chebyshevskii Sb., 23:5 (2022), 45–56
6.
D. V. Gorbachev, “Weighted Carleman inequality for fractional gradient”, Chebyshevskii Sb., 23:4 (2022), 152–156
7.
D. V. Gorbachev, “Boas conjecture on the axis for the Fourier–Dunkl transform and its generalization”, Chebyshevskii Sb., 23:4 (2022), 39–51
8.
N. N. Dobrovol'skii, D. V. Gorbachev, V. I. Ivanov, “About three-dimensional nets of Smolyak III”, Chebyshevskii Sb., 23:3 (2022), 249–254
9.
D. V. Gorbachev, D. R. Lepetkov, “Refinement of the mean angle estimation in the Feyesh Toth problem”, Chebyshevskii Sb., 23:3 (2022), 245–248
10.
D. V. Gorbachev, “Bernstein Inequality in $L^p$ on the Line with Power Weight for $p>0$”, Mat. Zametki, 111:2 (2022), 300–303; Math. Notes, 111:2 (2022), 308–311
D. V. Gorbachev, N. N. Dobrovol'skii, I. A. Martyanov, “Refinement of Bernstein–Nikolskii constant for the sphere with Dunkl weight in the case of octahedron group”, Chebyshevskii Sb., 22:5 (2021), 354–358
D. V. Gorbachev, “Sharp Bernstein–Nikolskii inequalities for polynomials and entire functions of exponential type”, Chebyshevskii Sb., 22:5 (2021), 58–110
D. V. Gorbachev, N. N. Dobrovol'skii, “Nikolskii–Bernstein constants in $L^{p}$ on the sphere with Dunkl weight”, Chebyshevskii Sb., 21:4 (2020), 302–307
D. V. Gorbachev, I. A. Martyanov, “Markov–Bernstein–Nikol'skii constants for polynomials in $L^{p}$-space with the Gegenbauer weight”, Chebyshevskii Sb., 21:4 (2020), 29–44
D. V. Gorbachev, I. A. Martyanov, “Bounds of the Nikol'skii Polynomial Constants in $L^{p}$ with Gegenbauer Weight”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:4 (2020), 126–137; Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S117–S127
D. V. Gorbachev, N. N. Dobrovolskii, “Extremal Nikolskii–Bernstein- and Turán-type problems for Dunkl transform”, Chebyshevskii Sb., 20:3 (2019), 394–400
D. V. Gorbachev, I. A. Martyanov, “Interrelation between Nikolskii–Bernstein constants for trigonometric polynomials and entire functions of exponential type”, Chebyshevskii Sb., 20:3 (2019), 143–153
D. V. Gorbachev, E. P. Ofitserov, “New approach to searching for string median and visualization of string clusters”, Chebyshevskii Sb., 20:2 (2019), 93–107
25.
D. V. Gorbachev, V. I. Ivanov, “Muckenhoupt conditions for piecewise-power weights in Euclidean space with Dunkl measure”, Chebyshevskii Sb., 20:2 (2019), 82–92
D. V. Gorbachev, V. I. Ivanov, “A Sharp Jackson Inequality in $L_p(\mathbb R^d)$ with Dunkl Weight”, Mat. Zametki, 105:5 (2019), 666–684; Math. Notes, 105:5 (2019), 657–673
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”, Mat. Sb., 210:6 (2019), 56–81; Sb. Math., 210:6 (2019), 809–835
D. V. Gorbachev, V. I. Ivanov, “Nikol'skii–Bernstein Constants for Entire Functions of Exponential Spherical Type in Weighted Spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:2 (2019), 75–87; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S24–S35
D. V. Gorbachev, V. I. Ivanov, “On the doubling condition for non-negative positive definite functions on on the half-line with power weight”, Chebyshevskii Sb., 19:2 (2018), 90–100
32.
D. V. Gorbachev, I. A. Martyanov, “On interrelation of Nikolskii Constants for trigonometric polynomials and entire functions of exponential type”, Chebyshevskii Sb., 19:2 (2018), 80–89
D. V. Gorbachev, V. I. Ivanov, E. P. Ofitserov, O. I. Smirnov, “The second Logan extremal problem for the fourier transform over the eigenfunctions of the Sturm–Liouville operator”, Chebyshevskii Sb., 19:1 (2018), 57–78
35.
D. V. Gorbachev, “Nikolskii - Bernstein constants for nonnegative entire functions of exponential type on the axis”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:4 (2018), 92–103
D. V. Gorbachev, V. I. Ivanov, E. P. Ofitserov, O. I. Smirnov, “Some extremal problems of harmonic analysis and approximation theory”, Chebyshevskii Sb., 18:4 (2017), 140–167
E. V. Larkin, D. V. Gorbachev, A. N. Privalov, “On the approximation of the flow of events for a Poisson”, Chebyshevskii Sb., 18:2 (2017), 222–234
38.
D. V. Gorbachev, V. I. Ivanov, “Some extremal problems for the Fourier transform over the eigenfunctions of the Sturm–Liouville operator”, Chebyshevskii Sb., 18:2 (2017), 34–53
D. V. Gorbachev, V. I. Ivanov, O. I. Smirnov, “Some Extremal Problems for the Fourier Transform
on the Hyperboloid”, Math. Notes, 102:4 (2017), 480–491
D. V. Gorbachev, V. I. Ivanov, “Approximation in $L_2$ by Partial Integrals of the Fourier Transform over the Eigenfunctions of the Sturm–Liouville Operator”, Mat. Zametki, 100:4 (2016), 519–530; Math. Notes, 100:4 (2016), 540–549
D. V. Gorbachev, V. I. Ivanov, R. A. Veprintsev, “Approximation in $L_2$ by partial integrals of the multidimensional Fourier transform in the eigenfunctions of the Sturm–Liouville operator”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:4 (2016), 136–152; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 97–113
D. V. Gorbachev, V. I. Ivanov, “Bohman extremal problem for the Jacobi transform”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:4 (2016), 126–135; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 88–96
D. V. Gorbachev, V. I. Ivanov, “Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type”, Mat. Sb., 206:8 (2015), 63–98; Sb. Math., 206:8 (2015), 1087–1122
D. V. Gorbachev, V. I. Ivanov, “Bohman extremal problem for the Dunkl transform”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:4 (2015), 115–123; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 88–96
D. V. Gorbachev, V. I. Ivanov, R. A. Veprintsev, “Optimal argument in the sharp Jackson inequality in the space $L_2$ with hyperbolic weight”, Math. Notes, 96:5 (2014), 904–913
D. V. Gorbachev, “An estimate of an optimal argument in the sharp multidimensional Jackson–Stechkin $L_2$-inequality”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:1 (2014), 83–91; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 70–78
A. V. Bondarenko, D. V. Gorbachev, “Minimal Weighted $4$-Designs on the Sphere $S^2$”, Mat. Zametki, 91:5 (2012), 787–790; Math. Notes, 91:5 (2012), 738–741
D. V. Gorbachev, M. V. Zakharova, “On an extremal problem for periodic functions with small support”, Mat. Zametki, 80:6 (2006), 940–942; Math. Notes, 80:6 (2006), 881–884
50.
D. V. Gorbachev, S. A. Strankovskii, “An extremal problem for even positive definite entire functions of exponential type”, Mat. Zametki, 80:5 (2006), 712–717; Math. Notes, 80:5 (2006), 673–678
V. I. Ivanov, D. V. Gorbachev, Yu. D. Rudomazina, “Some extremal problems for periodic functions with conditions on their values and Fourier coefficients”, Trudy Inst. Mat. i Mekh. UrO RAN, 11:2 (2005), 92–111; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S139–S159
D. V. Gorbachev, “An integral problem of Konyagin and the $(C,L)$-constants of Nikol'skii”, Trudy Inst. Mat. i Mekh. UrO RAN, 11:2 (2005), 72–91; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S117–S138
D. V. Gorbachev, A. S. Manoshina, “Turán Extremal Problem for Periodic Functions with Small Support and Its Applications”, Mat. Zametki, 76:5 (2004), 688–700; Math. Notes, 76:5 (2004), 640–652
D. V. Gorbachev, “A Sharpening of the Taikov Lower Bound in the Inequality between the $C$- and $L$-Norms for Trigonometric Polynomials”, Mat. Zametki, 74:1 (2003), 132–134; Math. Notes, 74:1 (2003), 123–126
D. V. Gorbachev, “An Extremum Problem for Periodic Functions with Small Support”, Mat. Zametki, 73:5 (2003), 773–778; Math. Notes, 73:5 (2003), 724–729
D. V. Gorbachev, V. I. Ivanov, “An extremum problem for polynomials related to codes and designs”, Mat. Zametki, 67:4 (2000), 508–513; Math. Notes, 67:4 (2000), 433–438
D. V. Gorbachev, “An extremum problem on a class of differentiable functions of several variables”, Mat. Zametki, 62:2 (1997), 192–205; Math. Notes, 62:2 (1997), 160–171
61.
D. V. Gorbachev, “Construction of the extremal function for a functional on the class $H_\omega^{(n)}$”, Mat. Zametki, 61:4 (1997), 519–529; Math. Notes, 61:4 (1997), 430–439
2022
62.
D. V. Gorbachev, I. A. Martyanov, “Delsarte problem for 4-designs on the unit 3-sphere”, Chebyshevskii Sb., 23:4 (2022), 157–161
Presentations in Math-Net.Ru
1.
Неравенство Бернштейна в $L_p$ со степенным весом при $p>0$ D. V. Gorbachev XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 30, 2024 18:20
Weight inequalities for the potential of Dunkl–Rissa D. V. Gorbachev, V. I. Ivanov XVI International Conference «Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history» dedicated to the 80th anniversary of the birth of Professor Michel Desa May 16, 2019 12:40
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