Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T16:29:50.506Z Has data issue: false hasContentIssue false
  • English
  • Français

EXPONENTIAL POLYNOMIAL APPROXIMATION OF WEIGHTED BANACH SPACE ON ℝn

Published online by Cambridge University Press:  02 August 2012

XIANGDONG YANG
XIANGDONG YANG*
Affiliation:
Department of Mathematics, Kunming University of Science and Technology, Kunming 650093, Yunnan Province, China e-mail: yangsddp@126.com
Rights & Permissions [Opens in a new window]

Abstract

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.

Necessary and sufficient conditions for the incompleteness of exponential system in Cα are characterised, where Cα is the weighted Banach space of complex continuous functions f defined on ℝn with f(t)exp(−α(t)) vanishing at infinity in the uniform norm.

Keywords

30E0541A30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 115 - 121
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Deng, G. T., Incompleteness and closure of a linear span of exponential system in a weighted Banach space, J. Approx. Theory 125 (2003), 1–9.CrossRefGoogle Scholar
2.Deng, G. T., Weighted exponential polynomial approximation, Sci. China 46 (2003), 280–287.Google Scholar
3.Deng, G. T., On weighted polynomial approximation with gaps, Nagoya Math. J. 178 (2005), 55–61.Google Scholar
4.Deng, G. T., Incompleteness and minimality of complex exponential system, Sci. China 50 (2007), 1–10.Google Scholar
5.Koosis, P., The logarithmic integral, vol. I (Cambridge University Press, Cambridge, UK, 1988).Google Scholar
6.Kroó, A., A geometric approach to the multivariate Müntz problem, Proc. Am. Math. Soc. 121 (1994), 199–208.Google Scholar
7.Levin, B. Ya., Distribution of zeros of entire functions (American Mathematical Society, Providence, RI, 1964).CrossRefGoogle Scholar
8.Malliavin, P., Sur quelques procédés d'extrapolation, Acta Math. 83 (1955), 179–255.CrossRefGoogle Scholar
9.Papush, D. E., On the growth of entire functions with ‘planar’ zeros, Teoriya Funktsii, Funktsional'nyi Analizi Ikh Prilozheniya 48 (1987), 117–125.Google Scholar
10.Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1987).Google Scholar
11.Yang, X. D., Incompleteness of exponential system in the weighted Banach space, J. Approx. Theory 153 (2008), 73–79.Google Scholar
12.Yang, X. D., On the completeness of the system t λn in C 0(E), J. Math. Anal. Appl. 368 (2010), 429–437.Google Scholar