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## Colloquium Mathematicum

1998 | 77 | 2 | 233-243
Tytuł artykułu

### Some Remarks on Rational Müntz Approximation on [0,∞)

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The following result is proved in the present paper: Let ${λ_{n}}$ be an increasing sequence of distinct real numbers which approaches a finite limit λ as n goes to infinity and for which $$\limsup_{n\to\infty}(λ-λ_{n})\root{3}οf{n}=\infty.$$ Then the rational combinations of ${x^{λ_{n}}}$ form a dense set in $C_{[0,∞]}$. One could note that the method used in this paper is probably more interesting than the result itself.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
233-243
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-12-08
Twórcy
autor
• Department of Mathematics, Hangzhou University, Hangzhou, Zhejiang 310028, P.R. China
Bibliografia
• [1] J. Bak and D. J. Newman, Rational combinations of $x^λ_k$, $λ_k$ ≥ 0 are always dense in C[0,1], J. Approx. Theory 23 (1978), 155-157.
• [2] E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, 1966.
• [3] G. Somorjai, A Müntz-type problem for rational approximation, Acta Math. Acad. Sci. Hungar. 27 (1976), 197-199.
• [4] Q. Y. Zhao and S. P. Zhou, Are rational combinations of {$x^λ_n$}, $λ_n$ ≥ 0, always dense in $C_[0,∞]$, Approx. Theory Appl. 13 (1997), no. 1, 10-17.
• [5] S. P. Zhou, On Müntz rational approximation, Constr. Approx. 9 (1993), 435-444.
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Bibliografia
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