Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T00:29:38.246Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Closure of the Linear Span of a Weighted Sequence in Lp(0, ∞)

Published online by Cambridge University Press:  20 November 2018

Jamil A. Siddiqi
Jamil A. Siddiqi*
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec; Université Paris-Sud, 91-Orsay, France
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let {λn} be an increasing sequence of positive numbers. The question of the closure in Lp(0, ∞ ) (1 ≦ p ≦ ∞ ) of the linear span of the sequence has been considered by several authors, notably by Boas (1) and Fuchs [3;4].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 386 - 396
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Boas, R. P., Jr., Density theorems for power series and complete sets, Trans. Amer. Math. Soc. 61 (1947), 54–68.Google Scholar
2. Boas, R. P., Jr., Entire functions (Academic Press, New York, 1954).Google Scholar
3. Fuchs, W. H. J., A theorem on finite differences with an application to the theory of Hausdorff summability, Proc. Cambridge Philos. Soc. 40 (1944), 189–196.Google Scholar
4. Fuchs, W. H. J., On the closure of ﹛e--ttαv﹜, Proc. Cambridge Philos. Soc. 42 (1946), 91–105.Google Scholar
5. Mandelbrojt, S., Séries adhérentes, régularisation des suites, applications (Gauthier-Villars, Paris, 1952).Google Scholar
6. Nachbin, L., Elements of approximation theory (Van Nostrand Company, Princeton, 1967).Google Scholar
7. Schwartz, L., Etudes des sommes d’ exponentielles (Hermann, Paris, 1958).Google Scholar
8. Siddiqi, J. A., Sur la quasi-analyticité généralisée et les problèmes qui s'y rattachent, D. Se. Thesis, Université de Paris, 1953.Google Scholar