Multivariate Davenport Series

Part of the Trends in Mathematics book series (TM)


We consider series of the form ∑a n {nx}, where nZ 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.


Hausdorff Dimension Hausdorff Measure Multifractal Analysis Arithmetic Function Jump Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors are grateful to Julien Brémont for pointing out a mistake in a first version of this chapter and to the anonymous referee for the careful reading and many valuable remarks.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques, UMR 8628Université Paris-SudOrsay CedexFrance
  2. 2.Laboratoire d’Analyse et de Mathématiques Appliquées UMR 8050Université Paris-Est - Créteil Val-de-MarneCréteil CedexFrance

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