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
- Gorbachev D, Ivanov V & Tikhonov S 2023, 'On the kernel of the (kappa, alpha)-generalized Fourier transform', Forum of Mathematics, Sigma, vol. 11 , e72.
- Kolomoitsev, Y, Lomako T & Tikhonov S 2023, 'Sparse Grid Approximation in Weighted Wiener Spaces', Journal Of Fourier Analysis And Applications, 29, 2, 19.
- Dai F, Prymak A, Shadrin A, Temlyakov V & Tikhonov S 2023, ‘On the cardinality of lower sets and universal discretization’, Journal of Complexity, 76, 101726.
- Dominguez O & Tikhonov S 2023, ‘Function spaces of logarithmic smoothness: embeddings and characterizations’, Memoirs Amer Math Soc, 282, 1393.
- Dyachenko M, Nursultanov E Tikhonov S & Weisz F 2023, ''Hardy-Littlewood-type theorems for Fourier transforms in Rd'', Journal of Function Analysis, vol. 284, no. 4, 109776.
Selected research activities
Research visits:
Oberwolfach Research Fellow,
MFO, Germany
Invited Researcher, IHES, Bures-sur-Yvette, France
Member of Editorial board:
Advances in Operator Theory
Analysis Mathematica
Journal of Fourier Analysis and Applications
Journal of Mathematical Analysis and Applications
Rendiconti del Circolo Matematico di Palermo
Seminar and Conference
talks:
International Conference on Multivariate Approximation,
Schloss Rauischholzhausen, Germany;
Seminar on Function Spaces, Friedrich-Schiller-Universität, Jena, Germany;
Colloquium, Universität zu Lübeck, Germany;
Analysis seminar, L.N.Gumilyov Eurasian National University, Astana, Kazakhstan.