space filling curves; pointwise Hölder regularity; Davenport series
Abstract :
[en] In this paper, we study the pointwise Hölder regularity of some spacefilling functions. In particular, we give some general results concerning the pointwise regularity of the Davenport series.
Disciplines :
Mathematics
Author, co-author :
Jaffard, Stéphane
Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Space-Filling Functions and Davenport Series
Publication date :
2010
Event name :
Fractals and Related Fields
Event place :
Monastir, Tunisia
Event date :
10-2007
Audience :
International
Main work title :
Recent Developments in Fractals and Related Fields
Editor :
Barral, Julien
Seuret, Stéphane
Publisher :
Birkhäuser, Boston, United States
ISBN/EAN :
978-0-8176-4887-9
Collection name :
Applied and Numerical Harmonic Analysis, 2010, Part 1
Bousch, T., Heurteaux, Y., Caloric measure on domains bounded by Weierstrass-type graphs (2000) Ann. Acad. Sci. Fenn., 25 (2), pp. 501-522
Cantor, G., Ein Beitrag zur Mannigfaltigkeitslehre (1878) J. Reine Angew. Math., 8, pp. 242-258
Clausel, M., Nicolay, S., Wavelets techniques for pointwise anti-Hölderian irregularity (2010) To Appear in Const. Approx.
Falconer, K., (1990) Fractal Geometry: Mathematical Foundation and Applications, , Wiley, Chichester
Fleron, J., A note on the history of the Cantor set and Cantor function (1994) Math. Mag., 67, pp. 136-140
Jaffard, S., Multifractal formalism for functions part I and II (1997) SIAM, 28, pp. 945-998
Jaffard, S., On Davenport expansions (2004) Proc. Symp. Pure Math., 72, pp. 273-303
Jaffard, S., Nicolay, S., Pointwise smoothness of space-filling functions (2008) Appl. Comput. Harmon. Anal., 26, pp. 181-199
Jaffard, S., Nicolay, S., (2008) On the Hölder Exponent of Some Historical Functions
Lebesgue, H., (1904) Leçons Sur l’intégration Et La Recherche De Fonctions Primitives. Gautiers-Villars, , Paris
Mandelbrot, B., Jaffard, S., Peano-Pólya motions, when time is intrinsic or binomial (Uniform or multifractal) (1997) Math. Intellig., 19, pp. 21-26
Morayne, M., On differentiability of Peano-type functions. I, II (1987) Colloq. Math., 53, pp. 133-135
Patil, S., Das, S., Nasipuri, A., Serial Data Fusion Using Space-Filling Curves in Wireless Sensor Networks (2005) Proc. IEEE Conf. SECON, Santa Clara, , CA
Peano, P., Sur une courbe, qui remplit toute une aire plane (1890) Math. Annal., 36, pp. 157-160
Quinqueton, J., Berthod, M., A locally adaptative Peano scanning algorithm (1981) IEEE Trans. Patt. Anal Mach. Intell., 3, pp. 403-412
Sagan, H., (1994) Space Filling Curves, , Springer, New York
Schoenberg, I.J., The Peano curve of Lebesgue (1938) Bull. AMS, 44, p. 519