Fourier transforms of Dini-Lipschitz functions
It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f. In general, if f(x) belongs to a certain function class, then the Lipschitz condition...
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Hindawi Limited
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000376 |
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doaj-f4e9c49f1a90448aa1b6cf0cf4c22c5d2020-11-24T23:13:34ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019230131210.1155/S0161171286000376Fourier transforms of Dini-Lipschitz functionsM. S. Younis0Department of Mathematics, Yarmouk University, Irbid, JordanIt is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f. In general, if f(x) belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms of f(x) belong. In the present work we do study the same phenomena for the wider Dini-Lipschitz class as well as for some other allied classes of functions.http://dx.doi.org/10.1155/S0161171286000376Dini-Lipschitz functionsFourier seriesFourier transforms. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. S. Younis |
| spellingShingle |
M. S. Younis Fourier transforms of Dini-Lipschitz functions International Journal of Mathematics and Mathematical Sciences Dini-Lipschitz functions Fourier series Fourier transforms. |
| author_facet |
M. S. Younis |
| author_sort |
M. S. Younis |
| title |
Fourier transforms of Dini-Lipschitz functions |
| title_short |
Fourier transforms of Dini-Lipschitz functions |
| title_full |
Fourier transforms of Dini-Lipschitz functions |
| title_fullStr |
Fourier transforms of Dini-Lipschitz functions |
| title_full_unstemmed |
Fourier transforms of Dini-Lipschitz functions |
| title_sort |
fourier transforms of dini-lipschitz functions |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1986-01-01 |
| description |
It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f. In general, if f(x) belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms of f(x) belong. In the present work we do study the same phenomena for the wider Dini-Lipschitz class as well as for some other allied classes of functions. |
| topic |
Dini-Lipschitz functions Fourier series Fourier transforms. |
| url |
http://dx.doi.org/10.1155/S0161171286000376 |
| work_keys_str_mv |
AT msyounis fouriertransformsofdinilipschitzfunctions |
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1725597893955420160 |