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The Fueter mapping theorem in integral form and the ℱ‐functional calculus
Author(s) -
Colombo Fabrizio,
Sabadini Irene,
Sommen Frank
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1315
Subject(s) - mathematics , calculus (dental) , pure mathematics , algebra over a field , medicine , dentistry
Abstract In this paper we show a version of the Fueter mapping theorem that can be stated in integral form based on the Cauchy formulas for slice monogenic (or slice regular) functions. More precisely, given a holomorphic function f of a paravector variable, we generate a monogenic function by an integral transform whose kernel is particularly simple. This procedure allows us to define a functional calculus for n ‐tuples of commuting operators (called ℱ‐functional calculus) based on a new notion of spectrum, called ℱ‐spectrum, for the n ‐tuples of operators. Analogous results are shown for the quaternionic version of the theory and for the related ℱ‐functional calculus. Copyright © 2010 John Wiley & Sons, Ltd.