# Titchmarsh convolution theorem

From Encyclopedia of Mathematics

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].

#### References

[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 |

**How to Cite This Entry:**

Titchmarsh convolution theorem.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Titchmarsh_convolution_theorem&oldid=32413

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article