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Results on singular distribution products of Mikusiński type

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Języki publikacji
EN
Abstrakty
EN
Results on products of Schwartz distributions are obtained when they have coinciding point singularities and only sums of the products exist in the distribution space. These results follow the pattern of a well-know distributional product published by Jan Mikusiński in 1966, and are named Mikusiński type products. The formulas are derived as the distributions are embedded in Colombeau algebra of generalized functions. This algebra possesses optimal properties regarding the distributional multiplication, and its notion of "association" allows one to obtain the results in terms of distributions.
Wydawca
Rocznik
Strony
49--61
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
  • Bulgarian Academy of Sciences INRNE - Theory Group 72 Tzarigradsko Shosse 1784 Sofia, Bulgaria, damyanov@netel.bg
Bibliografia
  • [1] Antonevich, A., Radyno, Ya., On a general method of constructing algebras of generalized functions, Soviet. Math. Dokl. 43(3) (1991), 680-684.
  • [2] Berg, L., Multiplication of distributions, Math. Nachr. 76 (1977), 195-202.
  • [3] Boie, V., Multiplication of distributions, Comment. Math. Univ. Carolin. 39(2) (1998), 309-321.
  • [4] Colombeau, J.-F., New Generalized Functions and Multiplication of Distributions, North-Holland Math. Stud. 84, Amsterdam, 1984.
  • [5] Damyanov, B., Results on Colombeau product of distributions, Comment. Math. Univ. Carolin. 43(4) (1997), 627-634.
  • [6] Damyanov, B., Multiplication of Schwartz distributions and Colombeau generalized functions, J. Appl. Anal., 5(2) (1999), 249-260.
  • [7] Damyanov, B., On the product of distributions in Colombeau algebra, Indian J. Math., 41(3) (1999), 91-95.
  • [8] Damyanov, B., On Colombeau distributional products of Mikusinski type, Indian J. Pure Appl. Math. 31(3) (2000) (to appear).
  • [9] Egorov, Yu., On the theory of generalized functions, Russian Math. Surveys 43(5) (1990), 1-49.
  • [10] Gel’fand, I., Shilov, G., Generalized Functions, Vol. 1, Academic Press, New York London, 1964.
  • [11] Friedlander, F., Introduction to the Theory of Distributions, Cambridge Univ. Press, Cambridge, 1982.
  • [12] Jelinek, J., Characterization of the Colombeau product of distributions, Comment. Math. Univ. Carolin. 27(2) (1986), 377-394.
  • [13] Jones, D., Generalized Functions, McGraw-Hill Publishing, London, 1966.
  • [14] König, H., Neue Begründung der Theorie der Distribution, Math. Nachr. 9 (1953), 129-148.
  • [15] Mikusinski, J., On the square of the Dirac delta-distribution, Bull. Polish Acad. Ser. Sci. Math. Astron. Phys. 43 (1966), 511-513.
  • [16] Oberguggenberger, M., Multiplication of Distributions and Applications to PDEs, Longman, Essex, 1992.
  • [17] Raju, C., Products and compositions with the Dirac delta function, J. Phys. A 43(2) (1982), 381-396.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0014-0004
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