Sergey Tikhonov

Centre de Recerca Matemàtica

Experimental Sciences & Mathematics

I was born in Russia in 1976. I graduated from the Lomonosov Moscow State University in 1999 and obtained my PhD in Mathematics from MSU in 2003. 2004-2006: Marie Curie Fellow at the Centre de Recerca Matemàtica, Barcelona. 2006-2008: Post-doctoral Fellow at the Scuola Normale Superiore, Pisa. 2008-September 2012: ICREA Researcher, CRM. From September 2012, I am an ICREA Research Professor at the Centre de Recerca Matemàtica. 2009: ISAAC Award. 2013: Humboldt Research Fellowship for Experienced Researchers.


Research interests

Mostly my research deals with Fourier Analysis and Approximation Theory. Particularly, I study the relationship between "smoothness" of a function and the possibility to approximate or to represent this function by a sum of "simple" functions. The case when "simple" functions have wave structure is of special interest.

Selected publications

- Nursultanov  E, Tikhonov S &  Tleukhanova N 2018 'Norm convolution inequalities in Lebesgue spaces', Rev Mat Iberoam, 34, 2, 811-838.  

- Dyachenko M & Tikhonov S 2018, ‘Smoothness and asymptotic  properties of functions with general monotone Fourier coefficients’, J. Fourier Anal. Appl., 24(4), 1072-1097.

- Dyachenko M, Nursultanov E & Tikhonov S 2018, ‘Hardy-type  theorems  on  Fourier  transforms  revised’, J Math Anal Appl, 467, 171-184.

- Dung D, Temlyakov V, Ullrich T & Tikhonov S (Ed.) 2018, Hyperbolic cross approximation, Advanced Courses in Mathematics – CRM Barcelona. Basel: Birkhäuser/Springer.  

- Gorbachev D, Liflyand E & Tikhonov S 2018, ‘Weighted norm inequalities for integral transforms’, Indiana Univ. Math. J., 67, 5, 1949-2003.  

- Gorbachev D & Tikhonov S 2018, ‘Wiener's problem for positive definite functions‘, Mathematische Zeitschrift, 289, 859-874.    

- Dyachenko M, Nursultanov E & Tikhonov S 2018, ‘Hardy--Littlewood and Pitt's inequalities for Hausdorff operators’, Bulletin des Sciences Mathématiques, 147, 40-57.

Selected research activities

PhD defenses in 2018:

-  Nestor Costa (UAB, co-directed with J. Bruna),

- Alberto Debernardi (UAB),

- Ainur Jumabayeva (UAB),

- Askhat Mukanov (UAB),

 - Yerzhan Toleugazy (Al-Farabi KazNU, co-directed with K. Bekmaganbetov).

Visiting Positions:  Invited Researcher, Institute of Mathematics of  Acad. of Sciences, Prague, Czech Republic.

Talks:  St.Petersburg Summer Meeting in Mathematical Analysis, St. Petersburg, Russia; Jaen Conference on Approximation Theory, Jaen, Spain; The Prague seminar on function spaces, Charles University, Prague, Czech Republic.

Colloquium talks: Pontificia Universidad Católica del Perú, Lima, Peru; Universidad Complutense de Madrid, Spain.

Member of Editorial board:  Analysis Mathematica, Journal of Mathematical Analysis and Applications, Demonstratio Mathematica, Jaen Journal on Approximation, Bulletin of Mathematical Analysis and Applications, Abstract and Applied Analysis.