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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 523618, 12 pages
New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series
Faculty of Mathematics and Computer Science, Paisii Hilendarski University of Plovdiv, 24 Tzar Assen Street, 4000 Plovdiv, Bulgaria
Received 11 February 2013; Accepted 22 April 2013
Academic Editor: Josip E. Pecaric
Copyright © 2013 Snezhana Georgieva Gocheva-Ilieva and Ivan Hristov Feschiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- N. Korneĭchuk, Exact Constants in Approximation Theory, vol. 38, chapter 3, 4, Cambridge University Press, New York, NY, USA, 1991.
- A. P. Prudnikov, A. Yu. Brychkov, and O. I. Marichev, Integrals and Series: Elementary Functions, chapter 5, CRC Press, Boca Raton, Fla, USA, 1998.
- J. Favard, “Sur les meilleurs precedes d'approximation de certaines classes de fonctions par des polynomes trigonometriques,” Bulletin des Sciences Mathématiques, vol. 61, pp. 209–224, 1937.
- S. R. Finch, Mathematical Constants, Cambridge University Press, New York, NY, USA, 2003.
- J. Bustamante, Algebraic Approximation: A Guide to Past and Current Solutions, Springer Basel AG, Basel, Switzerland, 2012.
- S. Foucart, Y. Kryakin, and A. Shadrin, “On the exact constant in the Jackson-Stechkin inequality for the uniform metric,” Constructive Approximation, vol. 29, no. 2, pp. 157–179, 2009.
- Yu. N. Subbotin and S. A. Telyakovskiĭ, “On the equality of Kolmogorov and relative widths of classes of differentiable functions,” Matematicheskie Zametki, vol. 86, no. 3, pp. 432–439, 2009.
- I. H. Feschiev and S. G. Gocheva-Ilieva, “On the extension of a theorem of Stein and Weiss and its application,” Complex Variables, vol. 49, no. 10, pp. 711–730, 2004.
- R. A. DeVore and G. G. Lorentz, Constructive Approximation, vol. 303, Springer, Berlin, Germany, 1993.
- V. P. Motornyĭ, “On sharp estimates for the pointwise approximation of the classes by algebraic polynomials,” Ukrainian Mathematical Journal, vol. 53, no. 6, pp. 916–937, 2001, Translation from Ukrains'kyi Matematychnyi Zhurnal, vol. 53, no. 6, pp. 783–799, 2001.
- W. Xiao, “Relative infinite-dimensional width of Sobolev classes ,” Journal of Mathematical Analysis and Applications, vol. 369, no. 2, pp. 575–582, 2010.
- P. C. Nitiema, “On the best one-sided approximation of functions in the mean,” Far East Journal of Applied Mathematics, vol. 49, no. 2, pp. 139–150, 2010.
- O. L. Vinogradov, “Sharp inequalities for approximations of classes of periodic convolutions by subspaces of shifts of odd dimension,” Mathematical Notes, vol. 85, no. 4, pp. 544–557, 2009, Translation from Matematicheskie Zametki, vol. 85, no. 4, pp. 569–584, 2009.
- A. V. Mironenko, “On the Jackson-Stechkin inequality for algebraic polynomials,” Proceedings of Institute of Mathematics and Mechanics, vol. 273, supplement 1, pp. S116–S123, 2011.
- V. F. Babenko and V. A. Zontov, “Bernstein-type inequalities for splines defined on the real axis,” Ukrainian Mathematical Journal, vol. 63, pp. 699–708, 2011.
- G. Vainikko, “Error estimates for the cardinal spline interpolation,” Journal of Analysis and its Applications, vol. 28, no. 2, pp. 205–222, 2009.
- O. L. Vinogradov, “Analog of the Akhiezer-Krein-Favard sums for periodic splines of minimal defect,” Journal of Mathematical Sciences, vol. 114, no. 5, pp. 1608–1627, 2003.
- L. A. Apaĭcheva, “Optimal quadrature and cubature formulas for singular integrals with Hilbert kernels,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ, no. 4, pp. 14–25, 2004.
- F. D. Gakhov and I. Kh. Feschiev, “Approximate calculation of singular integrals,” Izvestiya Akademii Nauk BSSR. Seriya Fiziko-Matematicheskikh Nauk, vol. 4, pp. 5–12, 1977.
- F. D. Gakhov and I. Kh. Feschiev, “Interpolation of singular integrals and approximate solution of the Riemann boundary value problem,” Vestsī Akadèmīī Navuk BSSR. Seryya Fīzīka-Matèmatychnykh Navuk, no. 5, pp. 3–13, 1982.
- B. G. Gabdulkhaev, “Finite-dimensional approximations of singular integrals and direct methods of solution of singular integral and integro-differential equations,” Journal of Soviet Mathematics, vol. 18, pp. 593–627, 1982.
- V. P. Motornyĭ, “Approximation of some classes of singular integrals by algebraic polynomials,” Ukrainian Mathematical Journal, vol. 53, no. 3, pp. 377–394, 2001.
- E. Vainikko and G. Vainikko, “Product quasi-interpolation in logarithmically singular integral equations,” Mathematical Modelling and Analysis, vol. 17, no. 5, pp. 696–714, 2012.
- H. Brass and K. Petras, Quadrature Theory: The Theory of Numerical Integration on a Compact Interval, vol. 178, American Mathematical Society, Providence, RI, USA, 2011.
- E. W. Weisstein, “Favard constants,” http://mathworld.wolfram.com/FavardConstants.html.
- A. G. Zygmund, Trigonometric Series, vol. 1, Cambridge University Press, 2nd edition, 1959.
- D. E. Knuth, The Art of Computer Programming. Vol. 1: Fundamental Algorithms, Section 1.2.11: Asymptotic Representations, Addison-Wesley, 3rd edition, 1997.
- S. Wolfram, The Mathematica Book, Wolfram Media, Champaign, Ill, USA, 5th edition, 2003.