Daniel Alpay Libros

Focusing on mathematical exercises, this collection guides readers through statistical physics, equilibrium thermodynamics, and information theory, highlighting their interconnections. It covers essential tools from linear algebra, functional analysis, and probability theory, applying them to topics like entropy, machine learning, and quantum channels. The text includes exercises from various domains, with notes providing motivation and hints or solutions for many. Aimed at senior undergraduates and beginning graduate students in mathematics, physics, or engineering, it prepares them for advanced studies.

Focusing on quaternionic linear operators, this work explores their unique properties compared to complex operators, particularly in the noncommutative realm. It introduces concepts like the S-spectrum and S-resolvent operators while examining de Branges spaces, which serve as quaternionic analogs of analytic function spaces. The study emphasizes specific reproducing kernels in the unit ball or half-space of quaternions, delving into Hilbert, Pontryagin, and Krein spaces and their connections to operator models.