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Sergey Tikhonov

Sergey Tikhonov

Centre de Recerca Matemàtica

Experimental Sciences & Mathematics

I graduated from the Lomonosov Moscow State University in 1999 and obtained the PhD degree in Mathematics from MSU in 2003. From September 2012, I am an ICREA Research Professor at the Centre de Recerca Matemàtica. 2003: PhD in Mathematics,  Lomonosov Moscow State University, Moscow. 2004-2006: Marie Curie Fellow at CRM, Barcelona. 2006-2008: Post-doctoral Fellow at the Scuola Normale Superiore, Pisa. 2008-September 2012: ICREA Researcher at CRM, Barcelona. 2009: ISAAC Award. 2012: ICREA Research Professor at CRM, Barcelona. 2013: Humboldt Research Fellowship for Experienced Researchers. 2021: Friedrich Wilhelm Bessel research prize

Research interests

My main research areas are 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

– Kolomoitsev Yu & Tikhonov S 2021 ‘Hardy-Littlewood and Ulyanov inequalities‘, Memoirs Amer. Math. Soc. vol. 271, no. 1325.

– Gorbachev DV, Ivanov VI & Tikhonov S 2021, ‘Riesz potential and maximal function for Dunkl transform‘, Potential Analysis, vol. 55, 513-538.

Tikhonov S 2021, ‘Weighted Fourier inequalities and boundedness of variations’, Proc Steklov Inst Math., 312, 1, 282 – 300.

– Dai F, Prymak A, Shadrin A, Temlyakov V & Tikhonov S 2021,`Sampling discretization of integral norms’, Constr. Approx., vol. 54, pp 455-47.

– Dai F, Gorbachev D & Tikhonov S 2021,`Estimates of the asymptotic Nikolskii constants for spherical polynomials’, Journal of Complexity, 65, 101553.

– Dai F, Prymak A, Shadrin A, Temlyakov V & Tikhonov S 2021,`Entropy numbers and Marcinkiewicz-type discretization theorem’, J. Functional Analysis, vol. 281, is. 6,  art. 109090.

– Belov A, Dyachenko M & Tikhonov S 2021, ‘Functions with general monotone Fourier coefficients’, Uspekhi Mat. Nauk/Russian Math. Surveys, vol. 76, no. 6 pp  3-70.

Selected research activities

Honors and Awards: Friedrich Wilhelm Bessel research prize by the Alexander von Humboldt Foundation

1 PhD Thesis defense (co-director)

Seminar talk: Université Claude Bernard Lyon 1, France.

Conference talks:  Approximation Theory and Applications, Moscow; Approximation and discretization, Moscow;
Georgian Mathematical Union, online; Conference on function spaces, Czech Republic; online; Discretization and related questions, Moscow, Russia.

Member of Editorial boards: Advances in Operator Theory, Analysis Mathematica, Journal of Fourier Analysis and Applications, Journal of Mathematical Analysis and Applications, Demonstratio Mathematica, Jaen Journal on Approximation, Bulletin of Mathematical Analysis and Applications.

ICREA Memoir 2021