Geodesic
On a class of generalized functions
Glasgow mathematical journal, Tome 17 (1976) no. 1, pp. 37-43

Voir la notice de l'article provenant de la source Cambridge University Press

Let be the complex linear space of all infinitely differentiable functions φ on the interval J = (a,b)(− ∞ ≦ a < 0 < b ≦ + ∞) such that φ(k)(0) = 0 for all non-negative integers k. Krabbe ([2], [3]) has defined a class of generalized functions on Jas an algebra M of linear operators on and has developed an operational calculus for these operators. Shultz ([6], Theorem 2.18) has recently shown that M is isomorphic to , where (resp. ) is the set of all distributions on J whose supports are contained in J+ = [0, b) (J- = (a,0]). In this paper we combine some of the ideas developed in [4] with results established in an earlier paper by Shultz to give an easier proof of the above result. Our methods also give a more direct proof of the main result (Theorem 1.22) of [2]. 
Rowlands, K. On a class of generalized functions. Glasgow mathematical journal, Tome 17 (1976) no. 1, pp. 37-43. doi: 10.1017/S001708950000269X
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