The delta function and the composition of distributions

• Autorzy: Fisher B.
• Języki publikacji: EN

Abstrakty

EN

Let F be a distribution and let / be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn{f)}, where Fn(x) = F(x) * 6n{x) and {6n(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function 6(x). The distribution 6(s)(xlamba+) is evaluated for lambda > 0 and s=0,1,2,....

Słowa kluczowe

EN

delta function; neutrix; neutrix limit

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 1
• Strony: 117--123
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Fisher B.

• Institute of Simulation Sciences, Serc, Hawthorn Building, De Montfort University, Leicester, LE1 9BH, England
• Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, England

Bibliografia

• [1] F. Al-Sirehy and B. Fisher, A composition of distributions, Internat J. Appl. Math., 1 (6) (1999), 689-694.
• [2] F. Al-Sirehy and B. Fisher, The composition of the functions [wzór], Fract. Calc. Appl. Anal. 2 (5) (1999), 575-582.
• [3] J . G. van der Corput, Introduction to the neutrix calculus, J . Analyse Math. 7 (1959), 291-398.
• [4] B. Fisher, On defining the change of variable in distributions, Rostock. Math. Kolloq. 28 (1985), 75-86.
• [5] B. Fisher, On defining the distribution [wzór] Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 15 (1985), 119-129.
• [6] B. Fisher, Neutrices and Distributions, Complex Analysis and Applications '87, Sofia 1989, 169-175.
• [7] I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. I, Academic Press, 1964.
• [8] B. Jolevska-Tuneska and B. Fisher, Results on the compositions of distributions, Internat. J . Appl. Math. 5 (4) (2001), 407-418.
• [9] J. D. Nicholas and B. Fisher, A result on the composition of distributions, Proc. (Math. Sci.), I.A.Sc., 109 (3) (1999), 33-42.