Date of birth: May 7, 1949
Place of birth: Moscow, Russia
In 1971 he graduated from the Faculty of Mechanics and Mathematics of the Odessa State University, and in 1974 – postgraduate studies at the Department of Mathematical Analysis of the Odessa University.
Candidate of Physical and Mathematical Sciences, dissertation “Coefficients of expansions in terms of bases of function spaces and representation of measurable functions by series” (Odessa State University, 1974).
Doctor of Physical and Mathematical Sciences, dissertation “Boundary Behavior and Differential Properties of Smooth Functions of Several Variables” (Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, 1990).
Scientific interests
- harmonic analysis
- approximation theory
- analysis on metric spaces with measure
- function spaces
- boundary value problems for partial differential equations
Publications
V.G. Krotov, Criteria for compactness in Lp spaces (in press)
V.G. Krotov, A.S. Lyalikov, LATEX. Computer system for preparing mathematical texts Minsk, BSU, 2010
V.G. Krotov, M.A. Prokhorovich, The rate of convergence of Steklov means on metric spaces with measure and the Hausdorff dimension, Mathematical notes, 2011, vol. 89, no. 1, pp. 145–148
V.G. Krotov, Quantitative form of Luzin’s C-property, Ukrainian Mathematical Journal, 2010, V.62, No.3, P.388-396
I.A. Ivanishko, V.G. Krotov, Compactness of Sobolev-type embeddings on metric measure spaces, Mathematicheskie Zametki, 2009, V.86, no. 6, pp. 829–844.
V.G. Krotov, M.A. Prokhorovich, Luzin’s approximation for Sobolev classes on metric spaces with measure, Izvestiya vuzov, matematika, 2008, no. 5, pp.55-66.
V.G. Krotov, Weighted Lp-inequalities for sharp-maximal functions on metric spaces with measure, Proceedings of the National Academy of Sciences of Armenia. Mathematics, 2006, Vol.41, No.2, C.27-42.
V.G. Krotov, L.V. Smovzh, Weighted estimates of the tangent boundary behavior, Mathematical Collection, 2006, V.197, No. 2, C.57-74.
I.A. Ivanishko, V.G. Krotov, Generalized Poincare-Sobolev inequality on metric spaces, Proceedings of the Institute of Mathematics of the National Academy of Sciences of Belarus, 2006, V.14, No. 1, P.51-61.
V.G. Krotov, Weighted Lp-inequalities for sharp-maximal functions, Doklady RAS, 2005, v.404, no.2, pp.155-158.
I.N. Katkovskaya, V.G. Krotov, A strong-type inequality for convolution with a square root from the Poisson kernel, Mathematical Notes, 2004, V.75, No. 4, C.580-591.
V.G. Krotov, When an orthogonal series is a Fourier series, Mathematical notes, 2003, V.74, No. 1, C.139-142.
V.G. Krotov, On the tangential boundary behavior of functions of several variables, Mathematical notes, 2000, V.62, No. 4, P.230-248.
V.G. Krotov, An exact estimate of the boundary behavior of functions from Hardy-Sobolev spaces in the critical case ap=n, Mathematical notes, 1997, V.62, No. 4, P.527-539.
V.G. Krotov, Inequalities for maximal Peano operators in a ball, Proceedings of the Institute of Mathematics of the National Academy of Sciences of Belarus, Sat. articles dedicated to the 60th anniversary of Prof. V.G. Sprindzhuk (1936-1987), Minsk, 1997, pp. 64-75.
V.G. Krotov, On the smoothness of the universal functions of Martsinkevich and universal trigonometric series, Izvestiya vuzov, mathematica, 1991, no. 8, pp. 26-31.
V.G. Krotov, An exact estimate of the boundary behavior of functions from Hardy-Sobolev spaces in the critical case ap=n, Reports of the Academy of Sciences of the USSR, 1991, V.319, No. 1, P.42-45.
V.G. Krotov, On the boundary behavior of functions from Hardy-type spaces, Proceedings of the Academy of Sciences of the USSR, Mathematical series, 1990, V.54, No. 5, P.957-974.
V.G. Krotov, Estimates for maximum operators associated with boundary behavior and their applications, Proceedings of the Mathematical Institute of the Academy of Sciences of the USSR, 1989, V.190, P.117-138.
V.G. Krotov, On differential properties on the boundary of functions that are holomorphic in the unit ball, Mathematical notes, 1989, V.45, No. 2, P.51-59.
V.G. Krotov, On the boundary behavior of fractional integrals of holomorphic functions in the unit ball, Izvestiya Vuzov, Mathematics, 1988, no. 4, P.73-75.
V.G. Krotov, On the smoothness of primitives N.N. Luzin and about the theorems of D.E. Menshov and N.K. Bari, Mathematical Collection, 1987, V.134, No. 3, C.404-420.
V.G. Krotov, E.A. Storozhenko, On the best approximations and derivatives of analytic functions from Hardy classes, In: “Research on the theory of approximation of functions”, Bashkir Branch of the Academy of Sciences of the USSR, Ufa, 1987.
V.G. Krotov, On differential properties of boundary functions from Hardy classes, Mathematische Nachrichten, 1986, V.126, P. 241-253.
V.G. Krotov, On differential properties of boundary functions from Hardy classes, Reports of the Academy of Sciences of the Ukrainian SSR, Ser.A, 1984, No. 6, P.15-18.
V.G. Krotov, On the unconditional basis property of the Haar system in the spaces Λ1w, Mathematical notes, 1982, V.32, No. 5, P.675-684.
V.G. Krotov, On the differentiability of functions from Lp and Hp, 0<p<1, Mathematical collection, 1982, V.117, No. 1, P.95-113.
V.G. Krotov, On the differentiability of functions from Lp and Hp, 0<p<1, Reports of the Academy of Sciences of the USSR, 1981, V.256, No. 6, P.1311-1314.
A.V. Bakhshetsyan, V.G. Krotov, On universal series in Schauder systems, Proceedings of the Academy of Sciences of the Armenian SSR, Mathematics series, 1981, V.16, No. 1, P.44-53.
V.G. Krotov, A note on the convergence of Fourier series in the spaces Hw, Acta Scientiarum Mathematicarum, 1979, V.41, Nos. 3-4, P.335-338.
V.G. Krotov, On the unconditional convergence of Fourier series in the Haar system in the spaces Hw, Mathematicheskie Zametki, 1978, V.23, No. 5, P.685-695.
V.G. Krotov, L. Leindler, On the strong summability of Fourier series and the classes Hw, Acta Scientiarum Mathematicarum, 1978, v. 40, no. 1-2, p. 93-98.
V.G. Krotov, Strong approximation by Fourier series and differentiability properties of functions, Analysis Mathematica, 1978, V.4, No. 3, C.199-214.
V.G. Krotov, Representation of measurable functions by Faber-Schauder series and universal series, Proceedings of the Academy of Sciences of the USSR, mathematical series, 1977, V.41, No. 1, C.215-29.
V.G. Krotov, On the multipliers of Fourier series with respect to Haar system, Analysis Mathematica, 1977, V.3, No.3, P.187-198.
V.G. Krotov, E.A. Storozhenko, P. Oswald, Direct and inverse theorems of Jackson type in the spaces Lp, 0<p<1, Doklady AN SSSR, 1976, V.266, no.1, P.44-47.
V.G. Krotov, E.A. Storozhenko, P. Oswald, Direct and inverse theorems of Jackson type in the spaces Lp,0<p<1, Mathematical collection, 1975, V.98, No. 3, S.395-415.
V.G. Krotov, On universal series according to the Faber-Schauder system, Bulletin of Moscow State University, series math.-mech. 1975, No. 4, S.53-58.
V.G. Krotov, On the Fourier coefficients with respect to one complete orthonormal system forming a basis in the space С(0,1), Izvestiya vuzov, mathematics, 1975, no. 10, pp. 33-46.
V.G. Krotov, Continuous functions with monotonically decreasing Fourier coefficients in the Haar system, Siberian Mathematical Journal, 1974, V.15, No. 2, P.439-444.
V.G. Krotov, Representation of measurable functions by Faber-Schauder series and universal series, Reports of the Academy of Sciences of the USSR, 1974, V.214, No. 6, P.1258-1261.
V.G. Krotov, On series in the Faber-Schauder system and in the bases of the space C(0,1), Mathematical notes, 1973, V.14, No. 2, P.185-195.
Educational materials
- Introduction to mathematics (lecture notes).
- Introduction to the theory of bases (lecture notes).
- Mathematical analysis (lecture notes).
- Applications of mathematical analysis in economics (lecture notes).
- Stochastic analysis of financial markets (lecture notes)