[Todos] Seminario de Análisis Funcional "Mischa Cotlar"

[jjgucci en dm.uba.ar]

El Instituto Argentino de Matemática “Alberto P. Calderón” tiene el agrado
de invitarlos al

Seminario de Análisis Funcional "Mischa Cotlar"

que se realizará el día viernes 14 de diciembre de 2012 a las 14 hs. en el
Salón del Instituto.



Expositora: Clothilde Melot – LAPT (CMI) Aix-Marseille Université



Título: "Study of an example of multifractal and "sparse" signal"









Resumen: In this talk we will review the fundamentals of multifractal
analysis and explain them with the help of an example: a family of
multifractal functions designed by S. Jaffard (1992). They can be considered
somehow as "sparse" signals since at each scale only few wavelet
coefficients of these signals do not vanish.

We study here their pointwise behavior, computing several pointwise
exponents (Hölder exponent, oscillating singularity exponent, local Lp
regularity) at every point and prove that from the point of view of each of
these exponents, the signals are multifractal indeed their pointwise
regularity is changing from point to point. Furthermore we will prove that
one can compute the Hausdorff dimension of the set of points at which the
signal has a given pointwise regularity with the help of a formula, the
so-called multifractal formalism, which uses global quantities for the
computation.



This work is a joint work with Claire Coiffard and Thomas Willer, LATP,
Marseille, France.









Cecilia Farias

Instituto Argentino de Matemática "Alberto P. Calderón"

Saavedra 15 3º piso

(C1083ACA) Buenos Aires

Argentina

Tel./Fax: (54) 11 4954-6781/2 int. 101.

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www.iam.conicet.gov.ar <http://www.iam.conicet.gov.ar/>





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