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.

Keywords

• monogenic functions
• slice monogenic functions
• plane waves
• W-functional calculus