# On Müntz rational approximation in multivariables

Colloquium Mathematicae (1995)

- Volume: 68, Issue: 1, page 39-47
- ISSN: 0010-1354

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topZhou, S.. "On Müntz rational approximation in multivariables." Colloquium Mathematicae 68.1 (1995): 39-47. <http://eudml.org/doc/210291>.

@article{Zhou1995,

abstract = {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 $C_\{I^s\}$.},

author = {Zhou, S.},

journal = {Colloquium Mathematicae},

language = {eng},

number = {1},

pages = {39-47},

title = {On Müntz rational approximation in multivariables},

url = {http://eudml.org/doc/210291},

volume = {68},

year = {1995},

}

TY - JOUR

AU - Zhou, S.

TI - On Müntz rational approximation in multivariables

JO - Colloquium Mathematicae

PY - 1995

VL - 68

IS - 1

SP - 39

EP - 47

AB - 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 $C_{I^s}$.

LA - eng

UR - http://eudml.org/doc/210291

ER -

## References

top- [1] J. Bak and D. J. Newman, Rational combinations of ${x}^{{\lambda}_{k}}$, ${\lambda}_{k}\ge 0$ are always dense in ${C}_{[0,1]}$, J. Approx. Theory 23 (1978), 155-157. Zbl0385.41007
- [2] E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, 1966. Zbl0161.25202
- [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. Zbl0631.41007
- [6] G. Somorjai, A Müntz-type problem for rational approximation, Acta Math. Acad. Sci. Hungar. 27 (1976), 197-199. Zbl0333.41012
- [7] S. P. Zhou, On Müntz rational approximation, Constr. Approx. 9 (1993), 435-444. Zbl0780.41010

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