Results on the Colombeau Products of the Distribution x + −r−1/2 with the Distributions x − −k−1/2 and x − k−1/2
- 6 Downloads
Results on the products of the distribution x + −r−1/2 with the distributions x − −k−1/2 and x − k−1/2 are obtained in the differential algebra G(ℝ) of Colombeau generalized functions, which contains the space D′(ℝ) of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in G(ℝ). This enables treating the results in terms of distributions again.
Key wordsdistribution Colombeau algebra Colombeau generalized functions multiplication of distributions
Unable to display preview. Download preview PDF.
- F. Farassat, “Introduction to generalized functions with applications in aerodynamics and aeroacoustics,” NASA Technical Paper 3428.Google Scholar
- J.-F. Colombeau, New Generalized Functions and Multiplication of Distribution, North Holland Math. Studies, vol. 84, North-Holland, Amsterdam, 1984.Google Scholar
- J.-F. Colombeau, Elementary Introduction to New Generalized Functions, North Holland Math. Studies, vol. 113, North-Holland, Amsterdam, 1985.Google Scholar
- M. Miteva and B. Jolevska-Tuneska, “Some results on Colombeau product of distributions,” Adv. Math. Sci. J., 1:2 (2012), 121–126.Google Scholar
- B. Jolevska-Tuneska and T. Atanasova-Pacemska, “Further results on Colombeau product of distributions,” Int. J. Math. Math. Sci., (2013), Article ID 918905; http://dx.doi.org/ 10.1155/2013/918905.Google Scholar
- M. Miteva, B. Jolevska-Tuneska, and T. Atanasova-Pacemska, “On products of distributions in Colombeau algebra,” Math. Probl. Eng. (2014), Article ID 910510; http://dx.doi.org/ 10.1155/2014/910510.Google Scholar
- M. Miteva, B. Jolevska-Tuneska, and T. Atanasova-Pacemska, “Colombeau Products of Distributions,” Springerplus, 5 (2016), 2042; http://dx.doi.org/10.1186/s40064-016-3742-8.Google Scholar
- K. Ohkitani and M. Dowker, “Burges equation with a passive scalar: dissipation anomaly and Colombeau calculus,” J. Math. Phys., 51:3 (2010), 033101.Google Scholar
- R. Steinbauer and J. A. Vickers, “The use of generalized functions and distributions in general relativity,” Classical Quantum Gravity, 23:10 (2006).Google Scholar