Kroó, András (2019) Weierstrass type approximation by weighted polynomials in Rd. JOURNAL OF APPROXIMATION THEORY, 246. pp. 85-101. ISSN 0021-9045
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Abstract
In this paper we consider weighted polynomial approximation on unbounded multidimensional domains in the spirit of the weighted version of the Weierstrass trigonometric theorem according to which every continuous function on the real line with equal finite limits at ±∞ is a uniform limit on R of weighted algebraic polynomials of degree 2n with varying weights (1+t2)−n. We will verify a similar statement in the multivariate setting for a general class of convex weights. We also consider the similar problem of multivariate polynomial approximation with varying weights for some typical non convex weights. In case of non convex weights of the form wα(x)≔(1+|x1|α+…+|xd|α)[Formula presented],0
| Item Type: | Article |
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| Uncontrolled Keywords: | Approximation by multivariate weighted polynomials; Homogeneous polynomials; Varying weights; Convex weights; Density |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 18 Oct 2019 06:34 |
| Last Modified: | 18 Oct 2019 06:34 |
| URI: | http://real.mtak.hu/id/eprint/102403 |
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