Open Access
October, 2016 A Fourier–Borel transform for monogenic functionals
Irene SABADINI, Franciscus SOMMEN
J. Math. Soc. Japan 68(4): 1487-1504 (October, 2016). DOI: 10.2969/jmsj/06841487


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.


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Irene SABADINI. Franciscus SOMMEN. "A Fourier–Borel transform for monogenic functionals." J. Math. Soc. Japan 68 (4) 1487 - 1504, October, 2016.


Published: October, 2016
First available in Project Euclid: 24 October 2016

zbMATH: 06669087
MathSciNet: MR3564441
Digital Object Identifier: 10.2969/jmsj/06841487

Primary: 30G35‎ , 42B10 , 46F15

Keywords: analytic functionals , Fourier–Borel transform , Lie ball , monogenic functionals

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 4 • October, 2016
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