Abstract
We consider extremum problems for entire functions of exponential spherical type related to important extremum problems on the optimal point (the Chernykh point) in the sharp jackson inequality in the spaceL 2(ℝn) and the connection between codes and designs on the torusT n.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. M. Nikol’skii,Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).
E. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J. (1971).
B. F. Logan, “Extremal problems for positive-definite bandlimited functions. II. Eventually negative functions,”SIAM J. Math. Anal.,14, No. 2, 253–257 (1983).
N. I. Chernykh, “On the Jackson inequality inL 2,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],88, 71–74 (1967).
N. I. Chernykh and V. V. Arestov, “On theL 2-approximation of periodic functions by trigonometric polynomials”, in:Approximation and Function Spaces. Proc. Inter. Conf. (Gdansk, 1979), North-Holland, Amsterdam (1981), pp. 25–43.
A. V. Moskovskii, “The Jackson theorems in the spacesL p (ℝn) andL p ,λ(ℝ+),”Izv. Tulsk. Gos. Univ., Math., Mech., Informatics,3, No. 1, 44–70 (1997).
E. E. Berdysheva, “Two related extremum problems for entire functions of several variables,”Mat. Zametki [Math. Notes],66, No. 3, 336–350 (1999).
H. Bateman and A. Erdélyi,Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York-Toronto-London (1953); Russian translation: Nauka, Moscow (1966).
A. G. Babenko, “The sharp Jackson-Stechkin inequality in the spaceL 2(ℝm),”Trudy Inst. Math. Mech. Ural Otdel. RAN,5, 182–198 (1998).
V. A. Yudin, “The location of points on the torus and the extremal properties of polynomials,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],219, 453–463 (1997).
B. F. Logan, “Extremal problems for positive-definite bandlimited functions. I. Eventually positive functions with zero integral functions”,SIAM J. Math. Anal.,14, No. 2, 253–257 (1983).
G. R. Grorev and Q. I. Rahman, “A quadrature formula with zeros of Bessel functions as nodes,”Math. Comput.,64, 715–725 (1995).
R. B. Chanem, “Explicit quadrature formulae for entire functions of exponential type”,J. Approximation Theory,92, 267–279 (1998).
A. I. Markushevich,The Theory of Analytic Functions, [in Russian], Vol. 2, Nauka, Moscow (1968).
V. A. Yudin, “The multidimensional Jackson theorem inL 2,”Mat. Zametki [Math. Notes],29, No. 2, 309–315 (1981).
V. A. Yudin, “Code and design,”Diskret. Mat. [Discrete Math. Appl.],9, No. 2, 3–11 (1997).
V. I. Ivanov, “On the approximation of functions in the spacesL p ,”Mat. Zametki [Math. Notes],56, No. 2, 15–40 (1994).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 179–187, August, 2000.
Rights and permissions
About this article
Cite this article
Gorbachev, D.V. Extremum problems for entire functions of exponential spherical type. Math Notes 68, 159–166 (2000). https://doi.org/10.1007/BF02675341
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02675341