The Hölder exponent of some Fourier series

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
Hauptverfasser: Chamizo, Fernando, Petrykiewicz, Izabela, Ruiz-Cabello, Serafín
Format: Artikel
Sprache:eng
Schlagworte:
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
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Zusammenfassung: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.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-016-9488-4