Abstract
We establish sufficient conditions for the extension of a function defined on [a, +∞), where a > 0, to a positive-definite function on the entire axis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. G. Krein, “On the problem of extension of Hermitian-positive continuous functions,” Dokl. Akad. Nauk SSSR, 26, No. 1, 17–20 (1940).
E. Lukacs, Characteristic Functions,Griffin, London (1970).
G. Pólya, “Ñber die Nullstellen gewisser ganzer Funktionen,” Math. Z., 2, 352–383 (1918).
R. M. Trigub, “Absolute convergence of Fourier integrals and summable Fourier series and approximation of functions on a torus by polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat., 44, No. 6, 1378–1409 (1980).
N. I. Akhiezer, Lectures on the Theory of Approximation [in Russian], Nauka, Moscow (1965).
B. Nagy, “Sur une classe generale de procedes de sommation pour les series de Fourier,” Acta Math., 14–52 (1948).
R. M. Trigub, “Absolute convergence of Fourier integrals and approximation of functions by linear means of their series,” in: Proceedings of the International Conference “Constructive Function Theory '81” (Varna, June 1–5, 1981) [in Russian], Bulgarian Academy of Sciences, Sofia (1983), pp. 178–180. (!-after in: everything is O.K. including '81)
R. M. Trigub, “Some properties of the Fourier transform of measure and their application,” in: Proceedings of the International Conference “Theory of Approximation of Functions” (Kiev, 1983) [in Russian], Nauka, Moscow (1987), pp. 439–443.
Rights and permissions
About this article
Cite this article
Zastavnyi, V.P. Extension of a Function from the Exterior of an Interval to a Positive-Definite Function on the Entire Axis and an Approximation Characteristic of the Class W r, β M . Ukrainian Mathematical Journal 55, 1189–1197 (2003). https://doi.org/10.1023/B:UKMA.0000010615.53499.b0
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000010615.53499.b0