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
- Dominguez O & Tikhonov S 2024, ‘Truncated smooth function spaces’, Trans. AMS, vol. 377, pp 8877-8934.
- Dominguez O, Li Y, Tikhonov S, Yang D & Yuan W 2024, 'A unified approach to self-improving property via K-functionals', Calc. Var. PDE, 63, 231.
- Pinos AD, Nursultanov E & Tikhonov S 2024, 'Fourier inequalities in Morrey and Campanato spaces', Journal of Functional Analysis, 287 - 7 -110522.
- V Ivanov, Gorbachev D & Tikhonov S 2024, ‘Logan's problem for Jacobi transforms’, Canadian Journal of Mathematics. 76, 3, pp 915-945.
- Gogatishvili A, Opic B, Tikhonov S & Trebels W 2024, 'A unified approach to inequalities for K-functionals and moduli of smoothness', Math. Z. 307 - 2 - 24.
Selected research activities
-Editorial: JMAA, JFAA, Analysis Math, Rendiconti del Circolo Matematico di Palermo, Advances in Operator Theory
-Main co-organizer of the Research program ``Discretization and recovery in high-dimensional spaces'' in the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
-Main co-organizer of the Workshop ``Multivariate approximation, discretization, and sampling recovery'', INI, Cambridge
-Main co-organizer of the conference ``Function spaces, analysis and approximation'' at the Nazarbayev University, Astana, Kazakhstan
Conference talks: Information theory, Boolean functions, and lattice problems, Hausdorff Institute, Bonn, Function Spaces, Differential Operators, and Nonlinear Analysis, Oberhof, International Conference of the Georgian Mathematical Union, Batumi, Tbilisi Analysis and PDE Workshop, Tbilisi, Fourier Analysis and its applications, Renyi Institute, Budapest
-Colloquium: Lezione lagrangiana, Università di Torino, Italy
-Seminar talks: Friedrich Schiller University Jena, Technische Universitat Chemnitz, L.N.Gumilyov Eurasian National University, Astana