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Summability of Hermite polynomial expansions of generalized functions

Published online by Cambridge University Press:  24 October 2008

Z. Ditzian
Z. Ditzian
Affiliation:
University of Alberta, Canada
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Extract

1. Introduction: The well-known result that every function f(x) ∈ L2(–∞, ∞) can be expanded in L2(– ∞,∞) by where and was recently followed by an expansion theorem for generalized functions. In papers by Wildlund(8), Giertz(4) and Zemanian(9) it was shown that a tempered distribution f∈S′ can be expanded by Hermite functions that is

for all ψ∈S (the space of rapidly decreasing test functions).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 129 - 139
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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