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

• Autorzy: S. P. Zhou
• 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 77
• Numer: 2
• Strony: 233-243

Daty

wydano

1998

otrzymano

1997-12-08

Twórcy

autor

S. P. Zhou

• 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.