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...
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, Fourier-sor |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16294 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 161-173 |
| ISSN: | 0001-6969 |