About the Uniform Hölder Continuity of Generalized Riemann Function

Bastin, Françoise; Nicolay, Samuel; Simons, Laurent

doi:10.1007/s00009-014-0501-3

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About the Uniform Hölder Continuity of Generalized Riemann Function

Bastin, Françoise; Nicolay, Samuel; Simons, Laurent

2016 • In Mediterranean Journal of Mathematics, 13 (1), p. 101-117

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/175527

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10.1007/s00009-014-0501-3

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Keywords :

Hölder continuity; Continuous Wavelet Transform; Riemann function

Abstract :

[en] In this paper, we study the uniform H\"{o}lder continuity of the generalized Riemann function~$R_{\alpha,\beta}$ (with $\alpha>1$ and $\beta>0$) defined by \[ R_{\alpha,\beta}(x)=\sum_{n=1}^{+\infty}\frac{\sin(\pi n^\beta x)}{n^\alpha},\quad x\in\mathbb{R}, \] using its continuous wavelet transform. In particular, we show that the exponent we find is optimal. We also analyse the behaviour of~$R_{\alpha,\beta}$ as $\beta$ tends to infinity.

Disciplines :

Mathematics

Author, co-author :

Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Simons, Laurent ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

About the Uniform Hölder Continuity of Generalized Riemann Function

Publication date :

2016

Journal title :

Mediterranean Journal of Mathematics

ISSN :

1660-5446

eISSN :

1660-5454

Publisher :

Springer

Volume :

Issue :

Pages :

101-117

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://link.springer.com/article/10.1007/s00009-014-0501-3

Available on ORBi :

since 24 December 2014

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