Extremum Problem for Periodic Functions Supported in a Ball
- D. V. Gorbachev
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We consider the Turan n-dimensional extremum problem of finding the value of An(hB n ) which is equal to the maximum zero Fourier coefficient \(\widehat f_0\) of periodic functions f supported in the Euclidean ball hB n of radius h, having nonnegative Fourier coefficients, and satisfying the condition f(0)= 1. This problem originates from applications to number theory. The case of A1([−h,h]) was studied by S. B. Stechkin. For An(hB n we obtain an asymptotic series as h → 0 whose leading term is found by solving an n-dimensional extremum problem for entire functions of exponential type.
- S. B. Stechkin, “An extremum problem for trigonometric series with nonnegative coefficients,” in: Selected Works. Mathematics [in Russian], Nauka, Moscow, 1998, pp. 244–245.
- N. N. Andreev, “Extremum problems for periodic functions with a small support,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] (1997), no. 1, 29–32.
- E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
- S. M. Nikol′skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow, 1977.
- H. Bateman and A. Erdélyi, Higher Transcendental Functions, vol. 1, McGraw-Hill, New York- Toronto-London, 1953.
- N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow, 1965.
- R. B. Ghanem and C. Frappier, “Explicit quadrature formulae for entire functions of exponential type,” J. Approx. Th., 92 (1998), 267–279.
- Extremum Problem for Periodic Functions Supported in a Ball
Volume 69, Issue 3-4 , pp 313-319
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- extremum problem
- periodic function
- Fourier coefficient
- asymptotic expansion
- entire function of exponential type
- Industry Sectors
- D. V. Gorbachev (1)
- Author Affiliations
- 1. Tula State University, Russia