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La Formule de Trotter-Kato by Cachia-V

La Formule de Trotter-Kato

by Cachia-V
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Book cover type: Paperback
  • ISBN13: 9786131533327
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 160
  • Original Price: GBP 41.0
  • Language: French
  • Edition: N/A
  • Item Weight: 245 grams
  • BISAC Subject(s): Functional Analysis

Les semi-groupes d'opérateurs jouent un rôle fondamental dans l'étude des équations d'évolution, et le cadre de ce travail, détaillé dans le premier chapitre, est le problème de Cauchy abstrait, linéaire, du premier ordre. L'approximation de Trotter-Kato permet, connaissant deux semi-groupes, de construire le semi-groupe engendré par la somme de leurs générateurs. Depuis 1990, différentes conditions ont été obtenues, assurant la convergence en norme d'opérateur de cette méthode pour des générateurs auto-adjoints dans un espace de Hilbert. Cette thèse étudie au contraire des semi-groupes holomorphes dont les générateurs ne sont pas auto-adjoints. Le premier ensemble de résultats comprend des estimations d'erreur en norme d'opérateur, dans le cadre de perturbations accrétives dans un espace de Banach ou de Hilbert. Ensuite sont présentés des résultats de convergence hors perturbation, pour des générateurs m-sectoriels, en norme d'opérateur et en norme de la trace. La dernière partie établit la méthode d'approximation de Chernoff en norme d'opérateur, notamment grâce à la notion nouvelle de contraction quasi-sectorielle, dans un espace de Hilbert.

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