Colombo F., Gantner J. Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes

Springer, 2019. — 327 p. — (Operator Theory: Advances and Applications 274). — ISBN: 978-3-030-16408-9.Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems.
These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields.Preliminary results
The direct approach to the S-functional calculus
The Quaternionic Evolution Operator
Perturbations of the generator of a group
The Phillips functional calculus
The H∞-Functional Calculus
Fractional powers of quaternionic linear operators
The fractional heat equation using quaternionic techniques
Applications to fractional diffusion
Historical notes and References
Appendix: Principles of functional Analysis