English
Some interactions between number theory and multifractal analysis
Virtualconference
Auteurs : Martin, Bruno (Auteur de la Conférence)
CIRM (Editeur )
11A55 - Continued fractions, {For approximation results, See 11J70; See also 11K50, 30B70, 40A15}
26A15 - "Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.), {For properties determined by Fourier coefficients, See 42A16; for those determined by approximation properties, See 41A25, 41A27}"
26A30 - Singular functions, Cantor functions, functions with other special properties
28A80 - Fractals
CIRM (Editeur )
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Résumé :
Some number-theoretic problems have led to the study of some infinite series that show multifractal behaviour, which means that their Hölder pointwise regularity may widely change from point to point. Reviewing some examples such as lacunary trigonometric series, Davenport series, Brjuno-type functions, I will put emphasis on the methods encountered in the literature to compute the pointwise Hölder exponent of such functions.
Keywords : irrationality exponent; Hölder exponent; wavelets; functional equations
Codes MSC : Keywords : irrationality exponent; Hölder exponent; wavelets; functional equations
11A55 - Continued fractions, {For approximation results, See 11J70; See also 11K50, 30B70, 40A15}
26A15 - "Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.), {For properties determined by Fourier coefficients, See 42A16; for those determined by approximation properties, See 41A25, 41A27}"
26A30 - Singular functions, Cantor functions, functions with other special properties
28A80 - Fractals
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 24/11/2020 Sous collection : Research talks arXiv category : Number Theory ; Dynamical Systems Domaine : Analysis and its Applications ; Number Theory Format : MP4 (.mp4) - HD Durée : 00:53:28 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-24_Martin.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19688003Citer cette vidéo: Martin, Bruno (2020). Some interactions between number theory and multifractal analysis. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19688003 URI : http://dx.doi.org/10.24350/CIRM.V.19688003 |
Voir aussi
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Bibliographie
