June 2022 The Weyl functional calculus in Michael-algebras
Lahcen Bouchikhi, Abdellah El Kinani
Rocky Mountain J. Math. 52(3): 805-816 (June 2022). DOI: 10.1216/rmj.2022.52.805

Abstract

We define and study a Weyl functional calculus for an n-tuple of commuting Paley–Wiener of r-exponential type elements of a Michael algebra. We show that this calculus preserves the same properties as in the Banach case. In particular, it is well defined for polynomials and gives results consistent with the natural algebraic definition. As applications, we obtain for bounded real numerical range series, two generalizations of P. Lévy theorems: the first one for Fourier series and the second for power series.

Citation

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Lahcen Bouchikhi. Abdellah El Kinani. "The Weyl functional calculus in Michael-algebras." Rocky Mountain J. Math. 52 (3) 805 - 816, June 2022. https://doi.org/10.1216/rmj.2022.52.805

Information

Received: 2 April 2021; Revised: 6 September 2021; Accepted: 6 September 2021; Published: June 2022
First available in Project Euclid: 16 June 2022

MathSciNet: MR4441098
zbMATH: 1501.46043
Digital Object Identifier: 10.1216/rmj.2022.52.805

Subjects:
Primary: 46H30 , 46J05

Keywords: Fourier inversion formula , joint spectrum , Michael-algebra , numerical range , P. Lévy’s theorem analogue , Paley–Wiener of r-exponential type , tempered distribution , Weyl functional calculus

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

Vol.52 • No. 3 • June 2022
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