On Müntz rational approximation in multivariables

• Autorzy: S. P. Zhou
• Języki publikacji: EN

Abstrakty

EN

The present paper shows that for any $s$ sequences of real numbers, each with infinitely many distinct elements, ${λ_{n}^{j}}$, j=1,...,s, the rational combinations of $x_{1}^{λ_{m_1}^1} x_{2}^{λ_{m_2}^2}...x_{s}^{λ_{m_s}^s}$ are always dense in $C_{I^s}$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1995
• Tom: 68
• Numer: 1
• Strony: 39-47

Daty

wydano

1995

otrzymano

1993-08-18

poprawiono

1994-03-30

Twórcy

autor

S. P. Zhou

• Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

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. G. Lorentz, Bernstein Polynomials, Toronto, 1953.
• [4] D. J. Newman, Approximation with Rational Functions, Amer. Math. Soc., Providence, R.I., 1978.
• [5] S. Ogawa and K. Kitahara, An extension of Müntz's theorem in multivariables, Bull. Austral. Math. Soc. 36 (1987), 375-387.
• [6] G. Somorjai, A Müntz-type problem for rational approximation, Acta Math. Acad. Sci. Hungar. 27 (1976), 197-199.
• [7] S. P. Zhou, On Müntz rational approximation, Constr. Approx. 9 (1993), 435-444.