On Müntz rational approximation in multivariables

Zhou, S.

Zhou, S.

Colloquium Mathematicae, Tome 68 (1995), p. 39-47 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $C_{I^{s}}$ .

Publié le : 1995-01-01

Zbl 0819.41014

EUDML-ID : urn:eudml:doc:210291

@article{bwmeta1.element.bwnjournal-article-cmv68i1p39bwm,
     author = {Zhou, S.},
     title = {On M\"untz rational approximation in multivariables},
     journal = {Colloquium Mathematicae},
     volume = {68},
     year = {1995},
     pages = {39-47},
     zbl = {0819.41014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p39bwm}
}

Zhou, S. On Müntz rational approximation in multivariables. Colloquium Mathematicae, Tome 68 (1995) pp. 39-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p39bwm/

Bibliographie

[000] [1] J. Bak and D. J. Newman, Rational combinations of $x^{λ_{k}}$ , $λ_{k} \geq 0$ are always dense in $C_{[0, 1]}$ , J. Approx. Theory 23 (1978), 155-157. | Zbl 0385.41007

[001] [2] E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, 1966. | Zbl 0161.25202

[002] [3] G. G. Lorentz, Bernstein Polynomials, Toronto, 1953.

[003] [4] D. J. Newman, Approximation with Rational Functions, Amer. Math. Soc., Providence, R.I., 1978.

[004] [5] S. Ogawa and K. Kitahara, An extension of Müntz's theorem in multivariables, Bull. Austral. Math. Soc. 36 (1987), 375-387. | Zbl 0631.41007

[005] [6] G. Somorjai, A Müntz-type problem for rational approximation, Acta Math. Acad. Sci. Hungar. 27 (1976), 197-199. | Zbl 0333.41012

[006] [7] S. P. Zhou, On Müntz rational approximation, Constr. Approx. 9 (1993), 435-444. | Zbl 0780.41010