On a nonlinear Peetre's theorem in full Colombeau algebras
نویسندگان
چکیده
منابع مشابه
A geometric approach to full Colombeau algebras
We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view on the construction of the intrinsically defined algebra Ĝ(M) on the manifold M given in [8]. MSC 2000: Primary: 46T30; secondary: 46F30.
متن کاملRegularity Theory in Colombeau Algebras
AMS Mathematics Subject Classification (2000): 35D05, 35L60, 46F30
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We define a general notion of set of indices which, using concepts from pre-ordered sets theory, permits to unify the presentation of several Colombeau-type algebras of nonlinear generalized functions. In every set of indices it is possible to generalize Landau’s notion of big-O such that its usual properties continue to hold. Using this generalized notion of big-O, these algebras can be formal...
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This contribution presents a comprehensive analysis of Colombeau (-type) algebras in the range between the diffeomorphism invariant algebra G = E M / N d introduced in Part I (see [Gro01]) and Colombeau’s original algebra G introduced in [Col85]. Along the way, it provides several classification results (again see [Gro01]) which are indispensable for obtaining an intrinsic description of a (ful...
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The Colombeau algebra of generalized functions allows to unrestrictedly carry out products of distributions. We analyze this operation from a microlocal point of view, deriving a general inclusion relation for wave front sets of products in the algebra. Furthermore, we give explicit examples showing that the given result is optimal, i.e. its assumptions cannot be weakened. Finally, we discuss t...
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ژورنال
عنوان ژورنال: Commentationes Mathematicae Universitatis Carolinae
سال: 2017
ISSN: 0010-2628,1213-7243
DOI: 10.14712/1213-7243.2015.197