Displaying similar documents to “On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)”

Results on generalized models and singular products of distributions in the Colombeau algebra 𝒢 ( ℝ )

Blagovest Damyanov (2015)

Commentationes Mathematicae Universitatis Carolinae

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Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea...

Distributionally regulated functions

Jasson Vindas, Ricardo Estrada (2007)

Studia Mathematica

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We study the class of distributions in one variable that have distributional lateral limits at every point, but which have no Dirac delta functions or derivatives at any point, the "distributionally regulated functions." We also consider the related class where Dirac delta functions are allowed. We prove several results on the boundary behavior of functions of two variables F(x,y), x ∈ ℝ, y>0, with F(x,0⁺) = f(x) distributionally, both near points where the distributional point value...

Singularities and normal forms of generic 2-distributions on 3-manifolds

B. Jakubczyk, M. Zhitomirskiĭ (1995)

Studia Mathematica

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We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases).

The elementary theory of distributions (I)

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...