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...
متن کاملDiffeomorphism invariant Colombeau algebras. Part II: Classification
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...
متن کاملWhy the Colombeau Algebras Cannot Handle Arbitrary Lie Groups ?
It is briefly shown that, due to the growth conditions in their definition, the Colombeau algebras cannot handle arbitrary Lie groups, and in particular, cannot allow the formulation, let alone, solution of Hilbert’s Fifth Problem. “History is written with the feet ...” Ex-Chairman Mao, of the Long March fame ... Science is not done scientifically, since it is mostly done by non-scientists ...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2018
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s001309151800010x