Abstract
We prove theorems on the extension of even-positive-definite functions from a finite interval to the entire axis and from a strip onto the entire plane.
References
M. G. Krein, “On the problem of extension of Hermite-positive continuous functions,”Dokl. Akad. Nauk SSSR,26, No. 1, 17–21 (1940).
M. G. Krein, “On Hermite operators with deficiency index equal to 1. I, II,”Dokl. Akad. Nauk SSSR,43, No. 8, 323–326 (1944);43, No. 8, 131–134 (1944).
M. G. Krein, “On one remarkable class of Hermite operators,”Dokl. Akad. Nauk SSSR. 44, No. 5, 191–195 (1944).
M. G. Krein, “Fundamentals of the theory of representation of Hermite operators with deficiency index (m, m),”Ukr. Mat. Zh.,1, No. 2, 3–66 (1949).
Yu. M. Berezanskii,Expansions in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965);English translation: Amer. Math. Soc. Transl., Vol. 17, Providence, R.I. (1968).
V. V. Gnedenko, “On characteristic functions,”Bull. Mosk. Univ. (A),1, No. 5, 17–18 (1937).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1577–1581, November, 1999.
Rights and permissions
About this article
Cite this article
Lopotko, O.V. On the extension of even-positive-definite functions of one and two variables. Ukr Math J 51, 1782–1786 (1999). https://doi.org/10.1007/BF02525265
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02525265