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Titlebook: Analysis and Geometry; MIMS-GGTM, Tunis, Tu Ali Baklouti,Aziz El Kacimi,Nordine Mir Conference proceedings 2015 Springer International Publ

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Analysis and Geometry978-3-319-17443-3Series ISSN 2194-1009 Series E-ISSN 2194-1017
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https://doi.org/10.1007/978-3-319-20651-6ased on the notion introduced in (Bahouri, Trends Math pp 1–15 (2013), [.]) of being .-oscillating with respect to a scale. The relevance of this theory is illustrated on several examples related to Orlicz spaces.
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https://doi.org/10.1007/978-1-4471-7332-8we ask whether such a holomorphic function can be uniformly approximated on smaller balls by functions that are holomorphic on the entire space. This turns out to be a subtle (open) question, whose (partial) resolution in the past 15 years played a central role in deeper investigations in complex analysis in Banach spaces.
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A Cauchy-Kovalevsky Theorem for Nonlinear and Nonlocal Equations,locally in time and globally in space. Furthemore, an estimate for the analytic lifespan is provided. To prove these results, the equation is written as a nonlocal autonomous differential equation on a scale of Banach spaces and then a version of the abstract Cauchy-Kovalevsky theorem is applied, wh
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On Microlocal Regularity for Involutive Systems of Complex Vector Fields of Tube Type in ,,l subellipticity (hence microlocal hypoellipticity) and maximal estimates for the systems first studied by F. Treves in (Treves, Ann. Math. .(2) (1976) and .(2) (1981), [.]) for which he gave a necessary condition for microlocal hypoellipticity. After him, many mathematicians studied such systems in
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Non-closed Range Property for the Cauchy-Riemann Operator,sary and sufficient conditions for the . closed range property for . on bounded Lipschitz domains in . with connected complement. It is proved for the Hartogs triangle that . does not have closed range for (0, 1)-forms smooth up to the boundary, even though it has closed range in the weak . sense. A
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