## Related Articles

- Further Results on Colombeau Product of Distributions. Jolevska-Tuneska, Biljana; Atanasova-Pacemska, Tatjana // International Journal of Mathematics & Mathematical Sciences;2013, p1
Results on Colombeau product of distributions x-r-1/2+ and x-r-1/2- are derived. They are obtained in Colombeau differential algebra G(R) of generalized functions that contains the space D' (R) of Schwartz distributions as a subspace and has a notion of "association" that is a faithful...

- On Products of Distributions in Colombeau Algebra. Miteva, Marija; Jolevska-Tuneska, Biljana; Atanasova-Pacemska, Tatjana // Mathematical Problems in Engineering;2014, p1
Results on products of distributions x+-k + and Î´ (p) (x) are derived. They are obtained in Colombeau differential algebra G(R) of generalized functions that contains the space D1 (R) of Schwartz distributions as a subspace. Products of this form are useful in quantum renormalization theory...

- Microlocal Analysis of Generalized Pullbacks of Colombeau Functions. Haller, Simon // Acta Applicandae Mathematica;Jan2009, Vol. 105 Issue 1, p83
In distribution theory the pullback of a general distribution by a C âˆž-function is well-defined whenever the normal bundle of the C âˆž-function does not intersect the wave front set of the distribution. However, the Colombeau theory of generalized functions allows for a pullback by an...

- A rigorous solution concept for geodesic and geodesic deviation equations in impulsive... Kunzinger, M.; Steinbauer, R. // Journal of Mathematical Physics;Mar1999, Vol. 40 Issue 3, p1479
Reports on the involvement of highly singular products of distributions of the geodesic and geodesic deviation equation for impulsive gravitational waves. Solution concept for the equations based on embedding the distributional metric into the Colombeau algebra of generalized functions.

- Solution of an abstract Cauchy problem with nonlinear and random perturbations in the Colombeau algebra. Melnikova, I.; Alekseeva, U. // Doklady Mathematics;Mar2013, Vol. 87 Issue 2, p193
The article presents a solution on the abstract quasilinear stochastic Cauchy problem. It offers an adaptation of Colombeau's approach to multiplying generalized functions and examines the nonlinear component on the Hilbert space. It discusses the construction of a differential algebra...

- Remarks on the distributional Schwarzschild geometry. Heinzle, J. Mark; Steinbauer, Roland // Journal of Mathematical Physics;Mar2002, Vol. 43 Issue 3, p1493
This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a Î´-distribution supported at r=0. Using generalized distributional geometry in the sense of...

- Bill Leithead is reading. // New Scientist;11/18/2000, Vol. 168 Issue 2265, p51
Reviews several books including 'Multiplication of Distributions,' by Jean Francois Colombeau, 'A Conspiracy of Hope,' by Michael Cannon, and 'The Scottish Nation 1700-2000,' by T.M. Devine.

- A LINEAR FIRST-ORDER HYPERBOLIC EQUATION WITH A DISCONTINUOUS COEFFICIENT: DISTRIBUTIONAL SHADOWS AND PROPAGATION OF SINGULARITIES. DEGUCHI, HIDEO // Electronic Journal of Differential Equations;2011, Vol. 2011, Special section p1
It is well-known that distributional solutions to the Cauchy problem for ut + (b(t, x)u)x = 0 with b(t, x) = 2H(x-t), where H is the Heaviside function, are non-unique. However, it has a unique generalized solution in the sense of Colombeau. The relationship between its generalized solutions and...

- NEW APPROACH TO TEMPERATE GENERALIZED COLOMBEAU FUNCTIONS. Delcroix, Antoine // Publications de l'Institut Mathematique;2008, Issue 98, p109
A new approach to the algebra GT of temperate nonlinear generalized functions is proposed, in which GT is based on the space OM endowed with is natural topology in contrary to previous constructions. Thus, this construction fits perfectly in the general scheme of construction of Colombeau type...

- Generalized Solutions to Semilinear Elliptic PDE with Applications to the Lichnerowicz Equation. Holst, Michael; Meier, Caleb // Acta Applicandae Mathematica;Apr2014, Vol. 130 Issue 1, p163
In this article we investigate the existence of a solution to a semi-linear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one encounters in studying the constraint equations in...