On some distributional multiplicative products
Susana Trione (1984)
Studia Mathematica
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Susana Trione (1984)
Studia Mathematica
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Benno Fuchssteiner (1984)
Studia Mathematica
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Jérôme Lemoine, Jacques Simon (1996)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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It is proved that any Banach valued distribution on a bounded set can be extended to all of if and only if it is a derivative of a uniformly continuous function. A similar result is given for distributions on an unbounded set. An example shows that this does not extend to Frechet valued distributions. This relies on the fact that a Banach valued distribution is locally a derivative of a uniformly continuous function. For sake of completeness, a global representation of a Banach valued...
Colombeau, J.F. (1982)
Portugaliae mathematica
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Jan Mikusiński, Roman Sikorski
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CONTENTS Introduction........................................................................................................... 3 § 1. The abstraction principle............................................................................... 4 § 2. Fundamental sequences of continuous functions......................................... 5 § 3. The definition of distributions........................................................................ 9 § 4. Distributions as a generalization of...
James Arthur (1989)
Compositio Mathematica
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Manchon, Dominique (1999)
Journal of Lie Theory
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Jan Mikusiński, Roman Sikorski
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CONTENTS Introduction................................................................................... 3 § 1. Terminology and notation.................................................................................... 4 § 2. Uniform and almost uniform convergence....................................................... 6 § 3. Fundamental sequences of smooth functions............................................... 6 § 4. The definition of distributions................................................................................