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.


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

– Tikhonov S & Yuditskii P 2020, ‘Sharp Remez inequality’, Constructive Approximation, vol.  52, no. 2, pp 233-246.

– Dyachenko M, Mukanov A & Tikhonov S 2020, ‘Hardy-Littlewood theorems for trigonometric series with general monotone coefficients’, Studia Math., 250, 3, 217 – 234.

– Nursultanov E & Tikhonov S 2020, ‘Wiener–Beurling spaces and their properties‘,  Bulletin des Sciences Mathématiques, vol. 159, art. 102825.

– Dai F, Gorbachev D & Tikhonov S 2020, ‘Nikolskii inequality for lacunary spherical polynomials’, Proc. Amer. Math. Soc. vol. 148,  pp 1169-1174.

– De Carli L, Gorbachev D &  Tikhonov S 2020. ‘Weighted gradient inequalities and unique continuation problems’, Calculus of Variations and PDE’s, 59, 3, 89.

– Kolomoitsev Y & Tikhonov S 2020, ‘Properties of moduli of smoothness in Lp(Rd)’, J. Approx. Theory, vol. 257, Article  105423.

– Nursulatnov E & Tikhonov S 2020, ‘Weighted Fourier inequalities in Lebesgue and Lorentz space’, Journal of Fourier Analysis and Applications, vol. 26, article 57.

– Dai F, Gorbachev D & Tikhonov S 2020,`Nikolskii inequality for lacunary spherical polynomials’, Journal d’Analyse Mathématique vol. 140,  pp 161-185.

– Gorbachev DV, Ivanov VI & Tikhonov S 2020, ‘Sharp approximation theorems and Fourier inequalities in the Dunkl setting’, J. Approx. Theory, 258, 105462.

– Gorbachev DV, Ivanov VI & Tikhonov S 2020, ‘Uncertainty principles for eventually constant sign bandlimited functions‘,  SIAM J. Math. Anal., vol. 52, no. 5, pp 4751–4782.

– Kolomoitsev Yu & Tikhonov S 2020 ‘Smoothness of functions vs. smoothness of approximation processes‘, Bull. Math. Sci. vol. 10, no. 3,  2030002.

– Dominguez O, Haroske D & Tikhonov S 2020, ‘Embeddings and characterizations of Lipschitz spaces’, J. Math. Pures Appl., vol. 144, pp 69-105.

Selected research activities

Editorial positions: JFAA, JMAA, Advances Operator Th., Analysis Math., Demonstratio M., Jaen J. Appr.

Talks: Barcelona, Brazil, Italy