Preface; Contents; Classes of de Branges Matrices and Corresponding de Branges Spaces; 1. Introduction; 2. Notation; 3. Reproducing kernel Hilbert spaces; 4. Entire de Branges matrices; 5. Subclasses of; 6. The class of strongly regular entire de Branges matrices; 7. Other directions; References; Divided Differences and Two-sided Polynomial Interpolation Over Quaternions; 1. Introduction; 2. Divided differences and related Sylvester identity; 3. Related questions; 3.1. The determinate case; 3.2. The structure of the solution set; 3.3. The sum of two ideals

3.4. The product-ideal interpolation scheme3.5. Further questions; References; Fischer Decomposition in Generalized Fractional Clifford Analysis; 1. Introduction; 2. Preliminaries; 2.1. Analysis in higher dimensions; 2.2. Generalized fractional derivatives; 3. Sommen-Weyl relations and Fractional Fischer decomposition; 3.1. Fractional Sommen-Weyl relations; 3.2. Fractional Fischer decomposition; 3.3. Explicit formulae; Acknowledgment; References; Free Products of C*-Probability Spaces from p-Adic Hecke Algebras; 1. Introduction; 1.1. Motivation and Background; 1.2. Overview; 2. Preliminaries

An Introduction to Fractional Powers of Quaternionic Operators and New Fractional Diffusion Processes1. Introduction; 2. Slice hyperholomorphicity and the S-functional calculus; 2.1. Slice hyperholomorphic functions; 2.2. Quaternionic linear operators and the S-functional calculus; 3. Fractional powers of quaternionic operators via the H∞- functional calculus; 3.1. The H∞-functional calculus for quaternionic operators; 3.2. Fractional powers via the H∞-functional calculus; 4. A new approach to fractional evolution via quaternionic operators; 4.1. An example with nonconstant coefficients