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Romanyuk, Anatolii Sergeevich

 Statistics Math-Net.Ru Total publications: 9 Scientific articles: 9

 Number of views: This page: 5133 Abstract pages: 7355 Full texts: 2896 References: 1464
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), 61–100
2. A. S. Romanyuk, “Priblizhenie klassov $B_{p,\theta}^r$ periodicheskikh funktsii mnogikh peremennykh lineinymi metodami i nailuchshie priblizheniya”, Matem. sb., 195:2 (2004), 91–116

http://www.mathnet.ru/eng/person13017
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List of publications on ZentralBlatt

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        ; Math. Notes, 94:3 (2013), 379–391 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      ; Math. Notes, 87:3 (2010), 403–415 2008 3. A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Mat. Sb., 199:2 (2008),  93–114        ; Sb. Math., 199:2 (2008), 253–275 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      ; Math. Notes, 82:2 (2007), 216–228 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        ; Izv. Math., 70:2 (2006), 277–306 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        ; Sb. Math., 197:1 (2006), 69–93 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      ; Sb. Math., 195:2 (2004), 237–261 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      ; Izv. Math., 67:2 (2003), 265–302 2002 9. A. S. Romanyuk, “Approximation of Classes of Periodic Functions in Several Variables”, Mat. Zametki, 71:1 (2002),  109–121        ; Math. Notes, 71:1 (2002), 98–109

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