Titchmarsh convolution theorem

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The convolution algebra of suitable functions or series has no zero divisors. See Operational calculus or [a2], [a3]. For related matters, such as ideals and homomorphisms of convolution algebras, see [a1].


[a1] S. Grabiner, "Weighted convolution algebras and their homomorphisms" J. Zamanek (ed.) , Functional Analysis and Operator Theory , Banach Centre (1994) pp. 175–190
[a2] A.A. Borichev, "A Titchmarsh type convolution theorem in the group $\mathbf Z$" Ark. Mat. , 27 : 2 (1989) pp. 179–187
[a3] I.V. Ostrovskii, "Generalization of the Titchmarsh convolution theorem and complex-valued measures uniquely determined by their restriction to a half-line" , Stability Problems for Stochastic Models , Lecture Notes Math. , 1155 , Springer (1985) pp. 256–283
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This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article