Journal of the Mathematical Society of Japan

A Fourier–Borel transform for monogenic functionals

Irene SABADINI and Franciscus SOMMEN

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Abstract

We discuss the Fourier–Borel transform for the dual of spaces of monogenic functions. This transform may be seen as a restriction of the classical Fourier–Borel transform for holomorphic functionals, and it transforms spaces of monogenic functionals into quotients of spaces of entire holomorphic functions of exponential type. We prove that, for the Lie ball, these quotient spaces are isomorphic to spaces of monogenic functions of exponential type.

Article information

Source
J. Math. Soc. Japan, Volume 68, Number 4 (2016), 1487-1504.

Dates
First available in Project Euclid: 24 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1477327223

Digital Object Identifier
doi:10.2969/jmsj/06841487

Mathematical Reviews number (MathSciNet)
MR3564441

Zentralblatt MATH identifier
06669087

Subjects
Primary: 30G35: Functions of hypercomplex variables and generalized variables 46F15: Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15] 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
Fourier–Borel transform Lie ball analytic functionals monogenic functionals

Citation

SABADINI, Irene; SOMMEN, Franciscus. A Fourier–Borel transform for monogenic functionals. J. Math. Soc. Japan 68 (2016), no. 4, 1487--1504. doi:10.2969/jmsj/06841487. https://projecteuclid.org/euclid.jmsj/1477327223


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