Sequence spaces with exponent weights. Realizations of Colombeau type algebras

Abstract : We give a description of various algebras of generalized functions based on the introduction of pseudo-ultranorms on spaces of sequences in given locally convex function algebras. We study sheaf properties of these algebras, needed for microlocal analysis, and also consider regularity theory, functoriality and different concepts of association and weak equality in a unified setting. Using this approach, we also give new results on embeddings of ultradistribution and hyperfunction spaces into corresponding algebras of generalized functions.
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https://hal.univ-antilles.fr/hal-00758044
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Antoine Delcroix, Maximilian F. Hasler, Stevan Pilipovic, Vincent Valmorin. Sequence spaces with exponent weights. Realizations of Colombeau type algebras. Dissertationes Mathematicae, International Publishing Service/IPS, 2007, 447, pp.1-73. ⟨10.4064/dm447-0-1⟩. ⟨hal-00758044⟩

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