Formal differentiation of absolutely convergent Fourier series and classical function classes
We study the differentiability properties of a function f with absolutely convergent Fourier series and the smoothness property of the rth derivative f( r \ where r is a given natural number. We give best possible sufficient conditions in terms of the Fourier coefficients of / to ensure that / ^ bel...
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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, Fourier-sor |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16294 |
| LEADER | 01479nab a2200241 i 4500 | ||
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| 005 | 20260310110824.0 | ||
| 008 | 161015s2009 hu o 000 eng d | ||
| 022 | |a 0001-6969 | ||
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Brown Gavin | |
| 245 | 1 | 0 | |a Formal differentiation of absolutely convergent Fourier series and classical function classes |h [elektronikus dokumentum] / |c Brown Gavin |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2009 | ||
| 300 | |a 161-173 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 75 No. 1-2 | |
| 520 | 3 | |a We study the differentiability properties of a function f with absolutely convergent Fourier series and the smoothness property of the rth derivative f( r \ where r is a given natural number. We give best possible sufficient conditions in terms of the Fourier coefficients of / to ensure that / ^ belongs either to one of the Lipschitz classes Lip(a) and lip(a) for some 0 < a < 1, or to one of the Zygmund classes Zyg(l) and zyg(l). These sufficient conditions are also necessary in the cases when the Fourier coefficients ck of / are real numbers such that either kck > 0 for all k or ck > 0 for all k. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika, Fourier-sor | ||
| 700 | 0 | 1 | |a Móricz Ferenc |e aut |
| 700 | 0 | 1 | |a Sáfár Zoltán |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/16294/1/math_075_numb_001_002_161-173.pdf |z Dokumentum-elérés |