Sergey Tikhonov

Centre de Recerca Matemàtica (CRM)

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

– Gorbachev D,  Ivanov V &  Tikhonov S 2016 ‘Pitt’s inequalities and uncertainty principle for generalized Fourier transform‘, International Mathematics Research Notices, vol. 2016, no. 23, pp. 7179-7200.

– Nursultanov E,  Ruzhansky M &  Tikhonov S 2016, ‘Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds‘,  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5) vol. XVI, pp 981-1017.

– Dai F & Tikhonov S 2016, ‘Weighted fractional Bernstein’s inequalities and their applications’, J. d’Analyse Math., vol. 129, no. 1, pp 33-68.

– Dai F, Feng H & Tikhonov S 2016, ‘Reverse Hölder’s inequality for spherical harmonics’, Proc. Amer. Math. Soc., vol. 144, no. 3, pp 1041-1051.

– Gorbachev D, Ivanov V & Tikhonov S 2016, ‘Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in L2’, Journal of Approximation Theory, vol. 202, no. 2, pp 109-118.

Selected research activities


– Journal of Mathematical Analysis and Applications,
– Analysis Mathematica,
– Abstract and Applied Analysis,
– Bulletin of Mathematical Analysis and Applications,
– The Scientific World Journal.

Main organizer of the Research program “Constructive Approximation  and Harmonic Analysis” in CRM

Conference organisation 

May 2-6: Main organizer of the Workshop on Function Spaces and High-dimensional Approximation,  Barcelona, Spain

May 30- June 4: Main organizer of the Advanced course on Constructive Approximation and Harmonic Analysis,  Barcelona, Spain

June 6-10: Main organizer of the Conference on Harmonic Analysis and Approximation Theory (HAAT 2016),  Barcelona, Spain

Colloquium talks

– Delft University of Technology, The Netherlands.
– Colloquium, Nepal Mathematical Society.
– Università degli Studi di Perugia, Italy.


– Functional Analysis Seminar, Université de Franche-Comté , Besançon, France.

– Mathematics of Computation, Hausdorff Center for Mathematics, Germany.

– Approximation Theory Seminar, Steklov Mathematical Institute, Moscow, Russia.

Research stay: Institute of Mathematics of Acad. of Sciences, Prague, Czech Republic