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Romanyuk, Anatolii Sergeevich

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Total publications: 9
Scientific articles: 9

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Romanyuk, Anatolii Sergeevich
Head Scientist Researcher
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 22.11.1955
E-mail: ,
Keywords: best approximation; hyperbolic Fourier sum; Kolmogorov width; linear width; best trigonometric approximation; bilinear approximation; trigonometric width; classes of periodic functions.

Subject:

Exact order estimates are obtained of approximation of Besov classes $B^r_{p, \theta}$ of periodic functions of several variables by trigonometric polynomials with harmonics from hyperbolic crosses. The orders are established of Kolmogorov, linear and trigonometric widthes of classes $B^r_{p, \theta}$ in space $L_p$, $1 \leq p, q \leq \infty$. Best $M$-term trigonometric and bilinear approximations of mentioned classes are investigated; in passing some results by Sobolev and Nikolsky in this direction are supplemented and specified. The algorithm is proposed of construction of subspaces of trigonometric polynomials realizing the orders of Kolmogorov widthes of classes of functions of several variables defined by generalized derivative.

Biography

Graduated from Faculty of Mathematics and Mechanics of I. Franko Lvov State University in 1978 (department of theory of functions). Ph. D. thesis was defended in 1988. D. Sci. thesis was defended in 1996. A list of my works contains more than 50 titles.

   
Main publications:
  1. A. S. Romanyuk, “Nailuchshie $M$-chlennye trigonometricheskie priblizheniya klassov Besova periodicheskikh funktsii mnogikh peremennykh”, Izv. RAN. Ser. matem., 67:2 (2003), 61100
  2. A. S. Romanyuk, “Priblizhenie klassov $B_{p,\theta}^r$ periodicheskikh funktsii mnogikh peremennykh lineinymi metodami i nailuchshie priblizheniya”, Matem. sb., 195:2 (2004), 91116

http://www.mathnet.ru/eng/person13017
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Publications in Math-Net.Ru
2013
1. A. S. Romanyuk, “Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables”, Mat. Zametki, 94:3 (2013),  401–415  mathnet  mathscinet  zmath  elib; Math. Notes, 94:3 (2013), 379–391  isi  scopus
2010
2. A. S. Romanyuk, “Approximation of Classes $B^r_{p,\theta}$ of Periodic Functions of One and Several Variables”, Mat. Zametki, 87:3 (2010),  429–442  mathnet  mathscinet  zmath; Math. Notes, 87:3 (2010), 403–415  isi  scopus
2008
3. A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Mat. Sb., 199:2 (2008),  93–114  mathnet  mathscinet  zmath  elib; Sb. Math., 199:2 (2008), 253–275  isi  scopus
2007
4. A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Mat. Zametki, 82:2 (2007),  247–261  mathnet  mathscinet  elib; Math. Notes, 82:2 (2007), 216–228  isi  scopus
2006
5. A. S. Romanyuk, “Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $B_{p, \theta}^r$”, Izv. RAN. Ser. Mat., 70:2 (2006),  69–98  mathnet  mathscinet  zmath  elib; Izv. Math., 70:2 (2006), 277–306  isi  scopus
6. A. S. Romanyuk, “Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions”, Mat. Sb., 197:1 (2006),  71–96  mathnet  mathscinet  zmath  elib; Sb. Math., 197:1 (2006), 69–93  isi  scopus
2004
7. A. S. Romanyuk, “Approximability of the classes $B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations”, Mat. Sb., 195:2 (2004),  91–116  mathnet  mathscinet  zmath; Sb. Math., 195:2 (2004), 237–261  isi  scopus
2003
8. A. S. Romanyuk, “Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables”, Izv. RAN. Ser. Mat., 67:2 (2003),  61–100  mathnet  mathscinet  zmath; Izv. Math., 67:2 (2003), 265–302  isi  scopus
2002
9. A. S. Romanyuk, “Approximation of Classes of Periodic Functions in Several Variables”, Mat. Zametki, 71:1 (2002),  109–121  mathnet  mathscinet  zmath  elib; Math. Notes, 71:1 (2002), 98–109  isi  scopus

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