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1. Function Spaces and Spectral Theories

2. Reproducing Kernel Hilbert Spaces

3. Quaternionic Linear Operators on a Hilbert Space

4. de Branges Spaces

5. Functions of a Quaternionic Variable

6. Several Quaternionic Variables

7. Slice Polyanalytic Functions

8. Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces

9. Slice Hyperholomorphic Bergman Spaces

10. Slice Hyperholomorphic Fock Space

11. Quaternionic Banach and Hilbert Spaces

12. Wiener Algebras

13. Slice Hyperholomorphic Hardy Spaces

14. A Survey on the Recent Advances in the Spectral Theory on the S-Spectrum

15. Spaces and Linear Fractional Transformations

16. The Characteristic Operator Function

17. Structure Theorems for Spaces

18. J-Contractive Functions

19. Operator Models

20. Rational Functions

21. Quaternions and Matrices

22. Slice Hyperholomorphic Functions

23. Preliminaries

24. Canonical Differential Systems

29. Introduction

31. The Phillips functional calculus

32. The fractional heat equation using quaternionic techniques

33. Fractional powers of quaternionic linear operators

34. The H ∞-Functional Calculus

35. Introduction

36. Perturbations of the generator of a group

37. Preliminary results

38. The direct approach to the S-functional calculus

39. Applications to fractional diffusion

40. The Quaternionic Evolution Operator

41. Appendix: Principles of functional Analysis

42. Historical notes and References

43. The F-Functional Calculus for Unbounded Operators

44. Quaternionic Operators on a Hilbert Space

45. Properties of the S-Functional Calculus for Bounded Operators

46. The F-Functional Calculus for Bounded Operators

47. The H ∞-Functional Calculus

48. The S-Functional Calculus for Unbounded Operators

49. Slice Hyperholomorphic Functions

50. The S-Spectrum and the S-Functional Calculus

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