On Müntz rational approximation in multivariables

S. Zhou

Colloquium Mathematicae (1995)

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

Abstract

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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 .

How to cite

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Zhou, 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

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  1. [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. Zbl0385.41007
  2. [2] E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, 1966. Zbl0161.25202
  3. [3] G. G. Lorentz, Bernstein Polynomials, Toronto, 1953. 
  4. [4] D. J. Newman, Approximation with Rational Functions, Amer. Math. Soc., Providence, R.I., 1978. 
  5. [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. [6] G. Somorjai, A Müntz-type problem for rational approximation, Acta Math. Acad. Sci. Hungar. 27 (1976), 197-199. Zbl0333.41012
  7. [7] S. P. Zhou, On Müntz rational approximation, Constr. Approx. 9 (1993), 435-444. Zbl0780.41010

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