The S-spectrum and the S-functional calculus

Colombo, F; Gantner, J; Kimsey, DP

doi:10.1007/978-3-030-03074-2_3

The S-spectrum and the S-functional calculus

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Abstract

© Springer Nature Switzerland AG 2018. The fundamental difficulty in developing a mathematically rigorous theory of quaternionic linear operators was the identification of suitable notions of quaternionic spectrum and quaternionic resolvent operator. In this chapter we study the properties of the S-spectrum and the S-resolvent operators, and we introduce the quaternionic S-functional calculus.