Monogenic plane waves and the W -functional calculus

Abstract

In this paper, we introduce some integral transforms that map slice monogenic functions to monogenic functions. We then show that one of these integral transforms, which is based on the Cauchy formula of slice monogenic functions, is useful to define a functional calculus depending on a parameter for n‐tuples of bounded operators. Copyright © 2015 John Wiley & Sons, Ltd.

Entire Slice Regular Functions

“…The F-functional calculus, see [18,41,63,67,68], which is based on the Fueter mapping theorem in integral form, is a monogenic functional calculus in the spirit of the one developed in [128,129,130,138,134], but it is associated to slice hyperholomorphicity. Finally the W-functional calculus, see [57], is a monogenic plane wave calculus based on slice hyperholomorphic functions.…”