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Convolutions as Bilinear and Linear Operators

Published online by Cambridge University Press:  20 November 2018

R. E. Edwards
R. E. Edwards*
Affiliation:
Institute of A dvanced Studies Australian National University
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Throughout this paper X denotes a fixed Hausdorff locally compact group with left Haar measure dx. Various spaces of functions and measures on X will recur in the discussion, so we name and describe them forthwith. All functions and measures on X will be scalarvalued, though it matters little whether the scalars are real or complex.

C = C(X) is the space of all continuous functions on X, Cc = Cc(X) its subspace formed of functions with compact supports. M = M(X) denotes the space of all (Radon) measures on X, Mc = MC(X) the subspace formed of those measures with compact supports. In general we denote the support of a function or a measure ξ by [ξ].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 275 - 285
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Schwartz, L., Théorie des distributions, II (Paris, 1951).Google Scholar
2. Wells, J., A note on the primes in a Banach algebra of measures, Pacific J. Math., 12 (1962), 1139–1144.Google Scholar