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Hilbert spaces of generalized functions extending L2, (II)

Published online by Cambridge University Press:  09 April 2009

J. B. Miller
J. B. Miller
Affiliation:
Australian National University, Canberra, A.C.T.
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The present note continues the discussion, begun in the first paper with the above title, of classes of spaces H which are extensions of L2 (0, ∞) and whose elements, which we call ‘sequence-functions’, exhibit some of the properties of distributions. The previous paper defined the spaces, and described how they can be used to extend the domain of definition of Waston transforms. Further related applications to transform theory are described in [2] and [3]. In this paper I pursue the analogy between these sequence- functions and other types of generalized functions further by discussing their local behaviour, the existence of ordinary and convolution-type products, and of derivatives and integrals.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 3 , August 1963 , pp. 267 - 281
Copyright
Copyright © Australian Mathematical Society 1963

References

[1]Miller, J. B., Hilbert spaces of generalized functions extending L2 (I), J. Aust. Math. Soc. 1 (1960), 281–298. To the references given at the end of [1] may be added:Google Scholar
[2]Miller, J. B., A class of series involving integral kernels, I and II, Math. Zeitschr. 76 (1961), 257–269 and 79 (1962), 227–236.Google Scholar
[3]Miller, J. B., On the solution of certain integral equations by generalized functions, Proc. Camb. Phil. Soc. 57 (1961), 767–777.CrossRefGoogle Scholar
[4]Miller, J. B., Normed spaces of generalized functions, Compositio Mathematica (to appear).Google Scholar