Abstract
We establish new conditions for the completeness of systems of exponentials with weight in L 2(ℝ), which complement and generalize the results obtained earlier by the authors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
B. V. Vinnitskii and A. V. Shapovalovskii, “On the completeness of systems of exponentials with weight,” Ukr. Mat. Zh., 41, No.12, 1695–1700 (1989).
B. V. Vinnitskii, “On zeros of certain classes of functions analytic in a half plane,” Mat. Stud., No. 6, 67–72 (1996).
R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain, American Mathematical Society, New York (1934).
P. Koosis, Introduction to Hp Spaces, Cambridge University Press, Cambridge (1980).
B. V. Vinnitskii, “On zeros of functions analytic in a half plane and completeness of systems of exponentials,” Ukr. Mat. Zh., 45, No.5, 484–500 (1994).
N. V. Govorov, Riemann Boundary-Value Problem with Infinite Index [in Russian], Nauka, Moscow (1986).
S. Mandelbrojt, Theorems on Closedness and Composition Theorems [in Russian], Inostrannaya Literatura, Moscow (1962).
P. Malliavin, “Sur quelques procédés d'extrapolation,” Acta Math., 93, No.3-4, 179–255 (1955).
W. N. J. Fuchs, “On the closure of {e-tta v},” Proc. Cambridge Phil. Soc., 18, No.2, 91–105 (1946).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vinnitskii, B.V., Shapovalovskii, A.V. A Remark on the Completeness of Systems of Exponentials with Weight in L2(ℝ). Ukrainian Mathematical Journal 52, 1002–1009 (2000). https://doi.org/10.1023/A:1005265314007
Issue Date:
DOI: https://doi.org/10.1023/A:1005265314007