01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Keywords:
Measures on infinite dimensional spaces, Gaussian measures, logarithmically concave measures, measurable polynomial, polynomial random variables, Nikolskii--Besov classes, Besov spaces
UDC:
519.21, 519.213, 517.51, 517.518.2
Subject:
Measure theory, probability theory, infinite dimensional analysis
Main publications:
Egor Kosov, “Fractional smoothness of images of logarithmically concave measures under polynomials”, Journal of Mathematical Analysis and Applications, 462:1 (2018), 390–406
Vladimir I. Bogachev, Egor D. Kosov, Georgii I. Zelenov, “Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy-Landau-Littlewood inequality”, Transactions of the American Mathematical Society, 370:6 (2018), 4401–4432
Egor D. Kosov, “Total Variation Distance Estimates via $L^2$-Norm for Polynomials in Log-concave Random Vectors”, International Mathematics Research Notices, 2021:21 (2021), 16492–16508
V. I. Bogachev, E. D. Kosov, G. I. Zelenov, “Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy-Landau-Littlewood inequality”, Transactions of the American Mathematical Society, 370:6 (2018), 4401-4432
E.D.Kosov, “Marcinkiewicz-type discretization of $L^p$-norms under the Nikolskii-type inequality assumption”, Journal of Mathematical Analysis and Applications, 504:1 (2021), 125358 , 32 pp.
Egor Kosov, “Fractional smoothness of images of logarithmically concave measures under polynomials”, Journal of Mathematical Analysis and Applications, 462:1 (2018), 390–406
Egor Kosov, “On fractional regularity of distributions of functions in gaussian random variables”, Fractional Calculus and Applied Analysis, 22:5 (2019), 1249–1268
E.D.Kosov, “Total Variation Distance Estimates via $L^2$-Norm for Polynomials in Log-concave Random Vectors”, International Mathematics Research Notices, 2021:21 (2021), 16492–16508
V.I. Bogachev, E.D. Kosov, and S.N. Popova, “A Characterization of Nikolskii–Besov Classes via Integration by Parts”, Doklady Mathematics, 96:2 (2017), 449–453
14.
E.D. Kosov, “A Characterization of Besov Classes in Terms of a New Modulus of Continuity”, Doklady Mathematics, 96:3 (2017), 587–590
15.
V. I. Bogachev, G. I. Zelenov, E. D. Kosov, “Membership of distributions of polynomials in the Nikolskii–Besov class”, Doklady Mathematics, 94:1 (2016), 453–457
16.
V. I. Bogachev, E. D. Kosov, I. Nourdin, G. Poly, “Two properties of vectors of quadratic forms of Gaussian random variables”, Theory Probab. Appl., 59:2 (2015), 208–221
17.
Egor Kosov, Vladimir Temlyakov, “Sampling discretization of the uniform norm and applications”, J. Math. Anal. Appl., 538:2 (2024), 128431 , 25 pp., arXiv: 2306.14207
Egor D. Kosov, “Remarks on Sampling Discretization of Integral Norms of Functions”, Proc. Steklov Inst. Math., 319 (2022), 188–198
20.
E.D. Kosov, “An Inequality between Total Variation and $L^2$ Distances for Polynomials in log-Concave Random Vectors”, Doklady Mathematics, 100:2 (2019), 423–425
21.
L. M. Arutyunyan, E. D. Kosov, I. S. Yaroslavtsev, “On some properties of polynomials measurable with respect to a Gaussian measure”, Doklady Mathematics, 90:1 (2014), 419–423
22.
V. I. Bogachev, E. D. Kosov, A. V. Shaposhnikov, “Regularity of solutions to Kolmogorov equations with perturbed drifts”, Potential Anal., 58 (2023), 681–702 , arXiv: 2104.04674
E. D. Kosov, “Distributions of Second Order Polynomials in Gaussian Random Variables”, Math. Notes, 111:1 (2022), 71–81
24.
V. I. Bogachev, E. D. Kosov, S. N. Popova, “On distributions of homogeneous and convex functions in Gaussian random variables”, Izv. Math., 85:5 (2021), 852–882
25.
Lavrentin Arutyunyan, Egor Kosov, “Deviation of polynomials from their expectations and isoperimetry”, Bernoulli, 24:3 (2018), 2043–2063
E. D. Kosov, V. N. Temlyakov, “Bounds for the sampling discretization error and their applications to the universal sampling discretization”, J. Complexity, 90 (2025), 101958 , 28 pp.
E. D. Kosov, “Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables”, Funct. Anal. Appl., 56:2 (2022), 101–109
30.
V.I. Bogachev, E.D. Kosov, S.N. Popova, “Densities of Distributions of Homogeneous Functions of Gaussian Random Vectors”, Doklady Mathematics, 102:3 (2020), 460–463
31.
L. M. Arutyunyan, E. D. Kosov, “Spaces of quasi-invariance of product measures”, Funct. Anal. Appl., 49:2 (2015), 142–144
32.
E. D. Kosov, “Lower estimates of measure of deviation of polynomials from mathematical expectations”, Doklady Mathematics, 92:3 (2015), 698–700
33.
E. D. Kosov, V. N. Temlyakov, “Sampling recovery of functions with mixed smoothness”, Adv. Oper. Theory, 10 (2025), 49 , 17 pp.
34.
E. D. Kosov, A. K. Zhukova, “Improved bounds for the total variation distance between stochastic polynomials”, Stoch. Proc. Appl., 170 (2024), 104279 , 15 pp.
35.
E. D. Kosov, “Regularity of Distributions of Sobolev Mappings in Abstract Settings”, Math. Notes, 114:5 (2023), 862–874
36.
Alexander V. Kolesnikov, Egor D. Kosov, “Moment measures and stability for Gaussian inequalities”, Theory Stoch. Process., 22(38):2 (2017), 47–61
37.
Arutyunyan L.M., Kosov E.D., “Sets of admissible shifts of convex measures”, Rendiconti Lincei-Matematica e Applicazioni, 26:1 (2015), 93–98
38.
E. D. Kosov, “Supports of measures with weak moments”, Doklady Mathematics, 86:3 (2012), 776–780
39.
P. A. Borodin, I. A. Ibragimov, B. S. Kashin, V. V. Kozlov, A. V. Kolesnikov, S. V. Konyagin, E. D. Kosov, O. G. Smolyanov, N. A. Tolmachev, D. V. Treshchev, A. V. Shaposhnikov, S. V. Shaposhnikov, A. N. Shiryaev, A. A. Shkalikov, “Vladimir Igorevich Bogachev (on his 60th birthday)”, Russian Math. Surveys, 76:6 (2021), 1149–1157
