On the density of homogeneous polynomials on regular convex surfaces
The classical Weierstrass theorem states that any function continuous on a compact set K c R d (d > 1) can be uniformly approximated by algebraic polynomials. In this paper we study a possible extension of this celebrated result for approximation by homogeneous algebraic polynomials on convex sur...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16293 |
| Tartalmi kivonat: | The classical Weierstrass theorem states that any function continuous on a compact set K c R d (d > 1) can be uniformly approximated by algebraic polynomials. In this paper we study a possible extension of this celebrated result for approximation by homogeneous algebraic polynomials on convex surfiices K C Rd such that K = —K. Here we make a major progress in a previous conjecture proving that functions continuous on regular O-symmetric convex surfaces can be approximated by a pair of homogeneous polynomials. Moreover, we settle completely the conjecture in Lp metric when 1 < p < oo. |
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| Terjedelem/Fizikai jellemzők: | 143-159 |
| ISSN: | 0001-6969 |