Multivariate Davenport series

Abstract : We consider series of the form $\sum a_n \{n\cdot x\}$, where $n\in\Z^{d}$ and $\{x\}$ is the sawtooth function. They are the natural multivariate extension of Davenport series. Their global (Sobolev) and pointwise regularity are studied and their multifractal properties are derived. Finally, we list some open problems which concern the study of these series.
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https://hal.archives-ouvertes.fr/hal-00696089
Contributor : Arnaud Durand <>
Submitted on : Thursday, May 10, 2012 - 5:17:39 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:04 PM
Long-term archiving on : Saturday, August 11, 2012 - 2:36:53 AM

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  • HAL Id : hal-00696089, version 1
  • ARXIV : 1205.2343

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Arnaud Durand, Stéphane Jaffard. Multivariate Davenport series. 2012. ⟨hal-00696089⟩

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