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Biography and education:

→ born 27 February 1955, Moscow.

→ graduated from Faculty of Mechanics and Mathematics, MSU, 1977;

→ graduated from Ph.D. school of Faculty of Mechanics and Mathematics, MSU, 1980;

→ PhD Thesis "Local smoothness of functions and Fourier decomposition", MSU, 1981.

→ Dr. Sci. Thesis "About monotonicity in theory of multiple trigonometric series", MSU, 1993;

→ since 1974 is a Professor of the Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University. Member of the Dissertation Council of Faculty of Mechanics and Mathematics in analysis.

Teaching:

→ since 1984 works at Faculty of Mechanics and Mathematics of MSU.

→ many times was the lecturer of fundamental courses "Measure and integral theory", "Theory of functions and functional analysis", "Real analysis", "Functional analysis" and conducted seminars on these courses.

→ the lecturer of special courses "Additional chapters of real analysis" (jointly with P.L. Ulyanov), "Trigonometric series", "Multiple trigonometric series", "Special trigonometric series", "Conjugate functions".

→ jointly with V.A. Skvortsov, T.P. Lukashenko and A.P. Solodov leads special seminar "Orthogonal and trigonometric series".

→ jointly with B.S. Kashin, S.V. Konyagin and B.I. Golubov leads research seminar in theory of functions.

Research:

He has trained 5 doctoral students. One of them, A.N. Bachvalov, later defended his doctoral thesis. He has published 116 articles and is the author of the student book "Real analysis"(jointly with P.L. Ulyanov) and "Real analysis in Exercises" (jointly with P.L. Ulyanov, A.N. Bakhvalov, K.S. Kazaryan, P. Sifuentes). In 1986 one of the M.I.Dyachenko's work was awarded a silver medal of VDNH USSR. He was awarded a government scholarship for outstanding scientists for three periods of three years (1994-1997, 1997-2000, 2000-2003). He many times leaded the RFFI grants and now leads a RNF grant. Many times he was the member of research groups of RFFI and scientific schools's grants. He worked at the Autonomous University of Madrid under Spanisch's government scholarship (01.10.2001-30.09.2002).

His main research interests are multiple trigonometric series. He established the series of new estimates on norms of multiple trigonometric polynoms with monotone coefficients in \(L_p\)-metric. He introduced a new type of convergency of multiple Fourier series and obtained some important results on it. He proved several theorems on convergence of various partial sums of Fourier series of functions of many variables of bounded general variation. Jointly with S.Yu. Tikhonov and E.D. Nursultanov he has published series of works devoted to the Hardi-Littlewood theorems and trigonometric series theory with general monotone coefficients.

Publications (recent):

2023

→ M. I. Dyachenko, K. A. Oganesyan, "Counterexamples to the Hardy–Littlewood Theorem for Generalized Monotone Sequences", Math. Notes, 113:3 (2023), 458–463, DOI.

→ E. D. Alferova, M. I. Dyachenko, "\(\alpha\)-monotone sequences and the Lorentz theorem", Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2 (2023), 63–67, DOI.

→ M. Dyachenko, E. Nursultanov, S. Tikhonov, F. Weisz, "Hardy–Littlewood-type theorems for Fourier transforms in \(\mathbb{R}^d\)", Journal of Functional Analysis, 284:4 (2023), 109776, DOI.

→ M. I. Dyachenko, A. P. Solodov, "Asymptotics of Sums of Sine Series with Fractional Monotonicity Coefficients", Analysis Mathematica, 49:1 (2023), 67–77, DOI.

2021

→ M. I. Dyachenko, "Asymptotics of Sums of Cosine Series with Fractional Monotonicity Coefficients", Math. Notes, 110:6 (2021), 894–902, DOI.

→ A. S. Belov, M. I. Dyachenko, S. Yu. Tikhonov, "Functions with general monotone Fourier coefficients", Russian Math. Surveys, 76:6 (2021), 951–1017, DOI.

2020

→ M. I. Dyachenko, A. Mukanov, S. Yu. Tikhonov, "Hardy–Littlewood theorems for trigonometric series with general monotone coefficients", Studia Math., 250:3 (2020), 217–234, DOI.

2019

→ M. I. Dyachenko, A. B. Mukanov, S. Yu. Tikhonov, "Smoothness of functions and Fourier coefficients", Sb. Math., 210:7 (2019), 994–1018, DOI.

→ M. I. Dyachenko, E. Nursultanov, S. Tikhonov, "Hardy-type theorems on Fourier transforms revised", Journal of Math. Anal. and Appl., 467 (2019), 171–184, DOI.

→ M. I. Dyachenko, A. Mukanov, S. Yu. Tikhonov, "Uniform convergence of trigonometric series with general monotone coefficients", Canadian Journal of Math., 71:6 (2019), 1445–1463, DOI.

2018

→ M. Dyachenko, E. Nursultanov, S. Tikhonov, "Hardy–Littlewood and Pitt’s inequalities for Hausdorff operators", Bulletin des Sciences Mathematics, 147 (2018), 40–57, DOI.

→ M. I. Dyachenko, S. Yu. Tikhonov, "Smoothness and asymptotic properties of functions with general monotone Fourier coefficients", Journal of Fourier Anal. and Appl., 24:4 (2018), 1072–1097, DOI.

2017

→ D. G. Dzhumabaeva, M. I. Dyachenko, E. D. Nursultanov, "On convergence of multiple trigonometric series with monotone coefficients", Siberian Math. J., 58:2 (2017), 205–214, DOI.

→ M. I. Dyachenko, A. Mukanov, E. D. Nursultanov, "A Boas-type theorem for alpha-monotone functions", Math. Scandinavica, 120:1 (2017), 39–58, DOI.