ISSN:
1432-1785
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The research of [3] is continued. After some preparations on topological tensor products of algebras and modules, including a theorem for continuous bilinear operations on spaces of vector-valued distributions (cf. L. Schwartz [13]), we define the convolution for elements ofE′(B) = L,(E(ℝN),B), where B denotes a complete locally pseudoconvex algebra with continuous multiplication. A Paley-Wiener-Schwartz theorem on the Fourier-Laplace transform (FLT) of vector-distributions enables us to reduce the convolution to a pointwise product of B-valued entire functions and to derive some properties of the convolution algebra ζ (B), *). Those elements of a complete m-convex algebra, for which the analytic functional calculus can be continued to (E′(B),*), are characterized by use of the FLT. In the last section, we look at representations of distributions in ζ or ℑ with values in a complete topological vector space E by means of analytic E-valued functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01527258
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