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On a class of generalized functions

Published online by Cambridge University Press:  18 May 2009

K. Rowlands
K. Rowlands
Affiliation:
Department of Pure Mathematics, University College of Wales, Aberystwyth
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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].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 1 , January 1976 , pp. 37 - 43
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

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