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Monogenic plane waves and the W ‐functional calculus
Author(s) -
Colombo Fabrizio,
Lávička Roman,
Sabadini Irene,
Souček Vladimír
Publication year - 2016
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.3491
Subject(s) - mathematics , functional calculus , cauchy distribution , bounded function , calculus (dental) , cauchy's integral formula , tuple , pure mathematics , mathematical analysis , algebra over a field , cauchy problem , discrete mathematics , initial value problem , medicine , dentistry
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.