The Hölder exponent of some Fourier series
In this paper we study the local regularity of fractional integrals of Fourier series using several definitions of the Hölder exponent. We especially consider series coming from fractional integrals of modular forms. Our results show that in general, cusp forms give rise to pure fractals (as opposed...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2017-08, Vol.23 (4), p.758-777 |
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| container_title | The Journal of fourier analysis and applications |
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| creator | Chamizo, Fernando Petrykiewicz, Izabela Ruiz-Cabello, Serafín |
| description | In this paper we study the local regularity of fractional integrals of Fourier series using several definitions of the Hölder exponent. We especially consider series coming from fractional integrals of modular forms. Our results show that in general, cusp forms give rise to pure fractals (as opposed to multifractals). We include explicit examples and computer plots. |
| doi_str_mv | 10.1007/s00041-016-9488-4 |
| format | Article |
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| subjects | Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Fourier series Integrals Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing |
| title | The Hölder exponent of some Fourier series |
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