The subject of this monograph is the quaternionic spectral theory
based on the notion of S-spectrum. With the purpose of giving a
systematic and self-contained treatment of this theory that has
been developed in the last decade, the book features topics like
the S-functional calculus, the F-functional calculus, the
quaternionic spectral theorem, spectral integration and spectral
operators in the quaternionic setting. These topics are based on
the notion of S-spectrum of a quaternionic linear operator. Further
developments of this theory lead to applications in fractional
diffusion and evolution problems that will be covered in a separate
monograph.
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