- Name: Alexander Ivanovich STEPANETS.
- Date of birth: May 24, 1942.
- Place of birth - Ukraine, Chernigiv
region.
- Gratuated Kiev
University in 1965 (speciality
- "Mathematics").
- Doctor of Sciences Degree, Physics &
Mathematics -1974.
- Corresponding Member of the National
Academy of Sciences of Ukraine
- 1998.
Principal scientific investigations of A.I.Stepanets belong to the following fields of mathematics:
- the theory of functions;
- approximation theory;
- Fourier series theory;
- harmonic analysis;
- boundary values of analytic functions;
- integral transformations.
- In A.I.Stepanets
scientific works the
method is developed for solution of extremal problems of
approximation theory of functions resulted in obtaining
of final solutions of Kolmogoroff problem for a series of
classical linear processes of summation of Fourier series
in one-dimensional as well as multidimansional cases. In
particular, he has found asymptotic equalities for
deviations of multiple rectangular Fourier sums and
spherical Riesz-Bochner sums on Holder classes of
functions of several variables. These investigations were
summed up in his monograph "Uniform approximations
by trigonometric polynomials". - Kiev: "Naukova
dumka", 1981. - 340 p.
- In 1982 A.I.Stepanets proposed a new approach to classification of
periodic functions based on transformations of series by
multiplicators and shifts of argument. This approach
permits to arrange a wide spectrum of periodic functions
including functions with divergent Fourier series,
functions of small smoothness, smooth, infinitely
differentiable as well as analytic and entire functions.
For new classes of functions, practically all main
problems of approximation theory were considered.
Obtained results have just the same degree of
completeness as early known results for functions
differentiable in Weyl sense. These investigations
grounded the monograph "Classification and
Approximation of Periodic Functions". - Dordrecht:
Kluwer, 1995 (Mathematics and Its Applications, Vol.333).
- 360 p. (Kiev: "Naukova dumka", 1987).
- Recently A.I.Stepanets has obtained a number of final results
connected with approximation of locally summable
functions defined on real axis, with approximation of
Cauchy type integrals on rectifiable Jordan curves and
with strong summability of orthogonal expansions of
summable functions.
- A.I.Stepanets is the author of some results and notions which
can be of interest for mathematics in general. In
particular,
- he inroduced the notion of the
derivative of a function generalizing the notion
of ordinary derivative as well as Weyl and
Sobolev derivatives;
- method was developed permitting to
obtain formulae for finding zeros of a number of
special functions with an arbitrary prescribed
accuracy; in particular, such formulae were found
for integral sine and cosine;
- new representations were found for
deviations of Fourier sums on classes of
differentiable functions.
Work address: Tereschenkivska Str.,3, KIEV,
01601, UKRAINE.
E-mail:
step@imath.kiev.ua
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