Polynomials close to 0 resp. 1 on disjoint sets
For disjoint compact subsets I, J of a real interval [A, B] construction is given for polynomials P-n of degree n = 1,2,... that approximate 0 on I and 1 on J with geometric rate, vanish (in a given order) at finitely many given points of I, take the value 1 (in a given order) at finitely given poin...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2020
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| Sorozat: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
482 No. 2 |
| doi: | 10.1016/j.jmaa.2019.123549 |
| mtmt: | 31431163 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/21007 |
| Tartalmi kivonat: | For disjoint compact subsets I, J of a real interval [A, B] construction is given for polynomials P-n of degree n = 1,2,... that approximate 0 on I and 1 on J with geometric rate, vanish (in a given order) at finitely many given points of I, take the value 1 (in a given order) at finitely given points of J, and otherwise lie in between 0 and 1 on [A, B] . When I and J consist of alternating intervals, then P-n can also be monotone on each subinterval of [A, B] \ (I U J) . Some further consequences (like approximation of piecewise constant functions or the trigonometric variant) are also considered. (C) 2019 Elsevier Inc. All rights reserved. |
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| Terjedelem/Fizikai jellemzők: | Terjedelem: 13-Azonosító: 123549 |
| ISSN: | 0022-247X |