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Ensembles parfaits et séries trigonométriques
Paperback
Series: HR.Hors Collec.
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ISBN10: 2705680098
ISBN13: 9782705680091
Publisher: Hermann
Pages: 244
Weight: 0.77
Height: 0.52 Width: 6.14 Depth: 9.21
Language: French
ISBN13: 9782705680091
Publisher: Hermann
Pages: 244
Weight: 0.77
Height: 0.52 Width: 6.14 Depth: 9.21
Language: French
Les ensembles parfaits du type de Cantor, comme les fonctions continues partout non dérivables à la Weierstrass, les courbes sans tangentes à la Von Koch, sont devenues les paradigmes de la géométrie fractale de Benoit Mandelbrot et acquièrent rapidement droit de cité en physique comme l'avait prévu, bien à l'avance, Jean Perrin. Les dimensions fractionnaires en particulier la dimension de Hausdorff et la dimension capacitaire, dont l'égalité selon Frostman fait l'objet d'un chapitre de ce livre deviennent familières aux mathématiciens et à beaucoup de non-mathématiciens. La première édition de ce livre, publiée en 1963, a longtemps été la référence principale à ce sujet. Aussitôt après 1963, d'excellents travaux ont été suscités par ce livre, en particulier ceux de Nicolas Varopoulos, de Robert Kaufman, d'Yves Meyer. Des notes et des contributions originales de Thomas Körner et de Russel Lyons font le point de la situation en 1986. À cette époque, deux grands outils étaient apparus comme essentiels dans l'analyse de Fourier, en particulier dans la théorie des ensembles d'unicité et de multiplicité les méthodes probabilistes et le point de vue de Baire. Aujourd'hui, le sujet des ensembles d'unicité est renouvelé par la considération des ensembles analytiques. Il est intéressant de voir comment ce vieux problème, posé dans la thèse de Cantor sur l'unicité du développement trigonométrique, a pu servir de banc d'essai, au cours de plus d'un siècle, à tant de bonnes mathématiques.
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