Nikolai Yu. Antonov
http://www.imm.uran.ru
Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation
Deputy Director for Scientific Problems
PhD (Phys., Math.), Professor
ScopusID: 56238062300
ResearcherID: N-3229-2017
ORCID ID: 0000-0002-8627-2749
Scientific interests: Theory of functions, approximation theory, Fourier series.
Scientific achievements: Results on convergence almost everywhere and estimates of the growth rate of sequences of partial sums of one-dimensional and multiple trigonometric Fourier series of functions from the Orlicz classes and some other functional classes are obtained, a number of related problems are also solved.
Main publications:
- Antonov N.Yu. Convergence of Fourier series // East Journal on Approximations, 1996. Vol. 2, no. 2. P. 187–196.
- Antonov N.Yu. Almost everywhere convergence over cubes of multiple trigonometric Fourier series // Izv. Math., 2004. Vol. 68, no. 2. P. 223–241. DOI: 10.1070/IM2004v068n02ABEH000472
- Antonov N.Yu. Integrability of the majorants of Fourier series and divergence of the Fourier series of functions with restrictions on the integral modulus of continuity // Math. Notes, 2004. Vol. 76, no. 5. P. 606–619. DOI: 10.1023/B:MATN.0000049660.29081.bc
- Antonov N.Yu. Estimates for the growth order of sequences of multiple rectangular Fourier sums of integrable functions // J. Math. Sci., 2015. Vol. 209, no. 1. P. 1–11. DOI: 10.1007/s10958-015-2481-7
- Antonov N.Yu. On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables // Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014. Vol. 14, no. 4(2). P. 497–505.
- Antonov N.Yu. On almost everywhere convergence for lacunary sequences of multiple rectangular Fourier sums // Proc. Steklov Inst. Math. (Suppl.). 2017. Vol. 296, suppl. 1. P. 43–59. DOI: 10.1134/S0081543817020055