Tikhonov, Sergey – ICREA Memoir 2021

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.