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ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS
(CAMBRIDGE UNIV PRESS, 2008)
We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started ...
NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2009)
We define intrinsic, natural and metrizable topologies T(Omega), T, T(s,Omega) and T(s) in G(Omega), (K) over bar, G(s)(Omega) and (K) over bar (s) respectively. The topology T(Omega) induces T, T(s,Omega) and T(s). The ...
Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data
(PERGAMON-ELSEVIER SCIENCE LTD, 2009)
In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the ...
On the Hilbert transform in the framework of generalized functions
(TAYLOR & FRANCIS LTDABINGDON, 2013-08-02)
In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz ...
Tempered generalized functions and Hermite expansions
(Pergamon-elsevier Science LtdOxfordInglaterra, 2011)
Differential calculus and integration of generalized functions over membranes
(SPRINGER WIENWIEN, 2012)
In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized ...
ON STOCHASTIC GENERALIZED FUNCTIONS
(World Scientific Publ Co Pte LtdSingaporeSingapura, 2011)
Time-dependent tempered generalized functions and Ito's formula
(Taylor & Francis LtdAbingdonInglaterra, 2014)
Strong solution of the stochastic Burgers equation
(Taylor & Francis LtdAbingdonInglaterra, 2014)
Composition for a class of generalized functions in Colombeau's theory
(2001-12-01)
In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a ...