Results 51 to 60 of about 602 (89)
Microlocal Properties of Basic Operations in Colombeau Algebras
Journal of Mathematical Analysis and Applications, 2001 In the class of Colombeau distributions the operation of unrestrictedly carrying out products of distributions is analyzed from a microlocal point of view. General inclusions of wave-front sets of products in this algebra are derived and exaples are given to show the optimality of these inclusions.
Hörmann, Günther, Kunzinger, Michael
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On systems of linear algebraic equations in the Colombeau algebra [PDF]
Mathematica Bohemica, 1999 Summary: From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a~solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra \(\overline {\mathbb R}\) of generalized real numbers. It is worth mentioning that the algebra \(\
Ligȩza, Jan, Tvrdý, Milan
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Algebraic Approach to Colombeau Theory
, 2014 We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions, and the set of regular distributions with $\mathcal C^\infty ...
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Axiomatic field theory and Hida-Colombeau algebras
, 2022 An axiomatic quantum field theory applied to the self-interacting boson field is realised in terms of generalised operators that allows us to form products and take derivatives of the fields in simple and mathematically rigorous ways. Various spaces are explored for representation of these operators with this exploration culminating with a Hida ...
Filinkov, Alexei, Fuss, Ian G.
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The ultrarelativistic Reissner–Nordstro/m field in the Colombeau algebra [PDF]
Journal of Mathematical Physics, 1997 The electromagnetic field of the ultrarelativistic Reissner–Nordstro/m solution shows the physically highly unsatisfactory property of a vanishing field tensor but a nonzero, i.e., δ-like, energy density. The aim of this work is to analyze this situation from a mathematical point of view, using the framework of Colombeau’s theory of nonlinear ...
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Colombeau's Algebra of full Generalized Numbers
, 2009 Let $\bar{\Kset}_f$ denote the commutative unital ring of Colombeau's full generalized numbers. This ring can be endowed with an ultra-metric in such a way that it becomes a topological ring. There are many interesting question about $\bar{\Kset}_f$ in the framework of Commutative Algebra and General Topology as well as of the superposition of these ...
Aragona, Jorge +2 more
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A geometric approach to full Colombeau algebras [PDF]
Banach Center Publications, 2010 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 $\hat{\mathcal G}(M)$ on the manifold $M$ given in (Grosser et al., Adv. Math. 166 (2002), 179--206).
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Opening Note: The Golden Jubilee of the Institute of Mathematics and Statistics of the University of São Paulo. [PDF]
Sao Paulo J Math Sci, 2022 Barrera J +4 more
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On a nonlinear Peetre's theorem in full Colombeau algebras [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2017 10 pages.
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Products of distributions in Colombeau algebra
Asian-European Journal of MathematicsIn this paper, we evaluate some products of distributions in Colombeau algebra of generalized functions. In the classical theory of Schwartz distributions, multiplication of distributions is not defined for two arbitrary singular distributions. The properties of the Colombeau algebra allow us to calculate products of singular distributions which are ...
Marija Miteva +3 more
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