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  • apam-2015-0049-aop

    Rights statement: Copyright © 2017 by Walter de Gruyter GmbH

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Operational calculus and integral transforms for groups with finite propagation speed

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/10/2017
<mark>Journal</mark>Advances in Pure and Applied Mathematics
Issue number4
Volume8
Number of pages19
Pages (from-to)265-283
Publication StatusPublished
Early online date25/05/17
<mark>Original language</mark>English

Abstract

Let A be the generator of a strongly continuous cosine family (cos tA)) on a complex Banach space E. The paper develops an operational calculus for integral transforms and functions of A using the generalized harmonic analysis assocaited to certain hypergroups. It is shown that characters of hypergroups which have laplace representation give rise to bounded operators on E. Examples include the Mellin trasnform and the Mehler--Fock transform. The paper uses functional caclulus for the cosine family that is associated with waves that travel at unit speed. The main results include an operational calculus theorem for Sturm--Liouville hypergroups with Laplace representation as well as analogues to the Kunze--Stein phenomenon in the hypergroup convolution setting.

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Copyright © 2017 by Walter de Gruyter GmbH