This book gathers contributions written by Daniel Alpays friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpays 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpays primary research interests.

The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

Classes of de Branges matrices and corresponding de Branges spaces.- Divided differences and two-sided polynomial interpolation over quaternions.- Fischer Decomposition in generalized fractional Clifford Analysis.- Free Products of C*-Probability Spaces from p-Adic Hecke Algebras.- An introduction to fractional powers of quaternionic operators and new fractional diffusion processes.- Finite-dimensional self-adjoint extensions of a symmetric operator with finite defect and their compressions.- On the structure of Hausdorff moment sequences of complex matrices.- On some extremal problems for analytic functions with constraints on real or imaginary parts.- A Burns-Krantz type theorem for pseudo-contractive mappings.- Spectral Convergence of Large Block-Hankel Gaussian Random Matrices.- Bernstein type Inequalities for Bicomplex Polynomials.- Finite unions of intervals, Part I.- Directing functionals and de Branges space completions in almost Pontryagin spaces.