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The H∞ Functional Calculus Based On The S-Spectrum For Quaternionic Operators And For N-Tuples Of Noncommuting Operators, Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini, Tao Qian
The H∞ Functional Calculus Based On The S-Spectrum For Quaternionic Operators And For N-Tuples Of Noncommuting Operators, Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini, Tao Qian
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we extend the H∞ functional calculus to quaternionic operators and to n-tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus, called S-functional calculus. The S-functional calculus has two versions one for quaternionic-valued functions and one for Clifford algebra-valued functions and can be considered the Riesz-Dunford functional calculus based on slice hyperholomorphicity because it shares with it the most important properties.
The S-functional calculus is based on the notion of S-spectrum which, in the case of quaternionic normal operators on a Hilbert space, is also the notion of spectrum that appears …