Topological Convolution Algebras

Authors

Daniel Alpay, Chapman UniversityFollow
Guy Salomon, Ben Gurion University of the Negev

Document Type

Article

Publication Date

2013

Abstract

In this paper we introduce a new family of topological convolution algebras of the form ⋃p∈NL2(S,μp), where S is a Borel semi-group in a locally compact group G, which carries an inequality of the type ∥f∗g∥p≤Ap,q∥f∥q∥g∥p for p>q+d where d pre-assigned, and Ap,q is a constant. We give a sufficient condition on the measures μp for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, volume 264, in 2013. DOI: 10.1016/j.jfa.2013.02.016

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Recommended Citation

D. Alpay and G. Salomon. Topological convolution algebras. Journal of Functional Analysis, vol. 264 (2013), pp. 2224-2244.

Peer Reviewed

1

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.