01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
24.05.1942
Keywords:
fourier series,
best approximations,
Kolmogorov width,
function spaces,
linear methods,
modulus of continuity,
best approximations of integrals by integrals of finite rank,
absolute convergence of integrals.
Subject:
The methods are developed allowing to solve one of the main problems of approximation theory - problem of Kolmogorov–Nikolsky on classes of functions defined by moduli of continuity. The classification of periodic and non-periodic functions defined on whole real axis is proposed. The new approach is proposed to solution of problems of approximation of analytic functions in jordan domains.
Biography
Graduated mechanical-mathematical faculty of Kiev T. G. Shevchenko University in 1965. Kandidate Dissertation — 1969. Doctor Dissertation —1975. Published more than 170 scientific works Supervisor of scientific seminar on theory of functions in the Institute of Mathematics of National Ukrainian Academy of Sciences.
In 2000 was awarded by M. V. Ostrogradsky prize for the series of papers on theory of functions (jointly with S. M. Nikolsky and N. P. Korneichuk)
Main publications:
Classification and Approximation of Periodic Functions. DORDRECH, Kluwer, 1995 (Mathem. And applic. Vol. 333). 360 p.
Uniform Approximations - by Trigonometric Polinomials.Utrecht, Boston, Koln, Tokyo, 2001. 483 p.
A. I. Stepanets, A. L. Shidlich, “Extremal problems for integrals of non-negative functions”, Izv. RAN. Ser. Mat., 74:3 (2010), 169–224; Izv. Math., 74:3 (2010), 607–660
2007
2.
A. I. Stepanets, “Extremal Problems for Numerical Series”, Mat. Zametki, 82:5 (2007), 736–755; Math. Notes, 82:5 (2007), 660–676
A. I. Stepanets, “Solution of the Kolmogorov–Nikol'skii problem for the Poisson integrals of continuous functions”, Mat. Sb., 192:1 (2001), 113–138; Sb. Math., 192:1 (2001), 113–139
A. I. Stepanets, “Approximation by Fourier operators of functions that are defined
on the real axis”, Dokl. Akad. Nauk SSSR, 303:1 (1988), 50–53; Dokl. Math., 38:3 (1989), 492–495
5.
N. L. Pachulia, A. I. Stepanets, “Strong summability of Fourier series on classes of $(\psi,\beta)$-differentiable functions”, Mat. Zametki, 44:4 (1988), 506–516; Math. Notes, 44:4 (1988), 758–764
A. I. Stepanets, “Approximations on classes of $(\psi,\beta)$-differentiable functions”, Dokl. Akad. Nauk SSSR, 293:4 (1987), 797–800
7.
A. I. Stepanets, “Best approximations of infinitely differentiable functions in the space $L_s$”, Mat. Zametki, 42:1 (1987), 21–32; Math. Notes, 42:1 (1987), 522–529
8.
A. I. Stepanets, “Approximation of periodic functions by Fourier sums”, Trudy Mat. Inst. Steklov., 180 (1987), 202–204; Proc. Steklov Inst. Math., 180 (1989), 239–241
1986
9.
A. I. Stepanets, “Classification of periodic functions and the rate of convergence of their Fourier series”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 101–136; Math. USSR-Izv., 28:1 (1987), 99–132
A. I. Stepanets, “Classes of periodic functions and the approximation of their
elements by Fourier sums”, Dokl. Akad. Nauk SSSR, 277:5 (1984), 1074–1077
N. N. Sorich, A. I. Stepanets, “Simultaneous approximation of periodic functions and their derivatives”, Mat. Zametki, 36:6 (1984), 873–882; Math. Notes, 36:6 (1984), 935–940
A. I. Stepanets, “Simultaneous approximation of a pair of conjugate functions”, Mat. Zametki, 34:5 (1983), 641–650; Math. Notes, 34:5 (1983), 811–816
1982
13.
A. I. Stepanets, “Suprema of Fourier coefficients on classes of continuous and differentiable functions of several variables”, Izv. Akad. Nauk SSSR Ser. Mat., 46:3 (1982), 650–665; Math. USSR-Izv., 20:3 (1983), 611–624
A. I. Stepanets, “Sharp estimates of Fourier coefficients on classes of continuous and differentiable periodic functions of several variables”, Dokl. Akad. Nauk SSSR, 261:1 (1981), 34–38
A. I. Stepanets, “Simultaneous approximation of periodic functions and their derivatives by Fourier sums”, Dokl. Akad. Nauk SSSR, 254:3 (1980), 543–544
A. I. Stepanets, “Estimates of the deviations of partial Fourier sums on classes of continuous periodic functions of several variables”, Izv. Akad. Nauk SSSR Ser. Mat., 44:5 (1980), 1150–1190; Math. USSR-Izv., 17:2 (1981), 369–403
N. N. Zaderei, A. I. Stepanets, “Approximation of Fourier sums on classes of periodic functions that are defined by polyharmonic operators”, Mat. Zametki, 27:4 (1980), 569–581; Math. Notes, 27:4 (1980), 280–286
1977
18.
A. I. Stepanets, “Approximation by Riesz sums of periodic functions of Hölder classes”, Mat. Zametki, 21:3 (1977), 341–354; Math. Notes, 21:3 (1977), 190–198
A. I. Stepanets, “Approximation of continuous periodic functions of many variables by spherical Riesz means”, Mat. Zametki, 15:5 (1974), 821–832; Math. Notes, 15:5 (1974), 492–498
A. I. Stepanets, “The approximation of continuous periodic functions of two variables by Faward sums”, Mat. Zametki, 13:5 (1973), 655–666; Math. Notes, 13:5 (1973), 394–400
A. I. Stepanets, “Deviation of partial sums of Fourier series in Hölder classes of functions of two variables”, Dokl. Akad. Nauk SSSR, 206:3 (1972), 549–551
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