Harmonic Analysis on Symmetric Spaces-Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane

The book "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane" offers a comprehensive introduction to harmonic analysis on fundamental symmetric spaces. It is aimed at graduate-level mathematics students as well as researchers in the fields of physics and engineering. The author, Audrey Terras, employs an informal writing style that emphasizes motivation, illustrative examples, historical contexts, and, above all, practical applications in mathematics, statistics, physics, and engineering. The second edition of the book includes numerous corrections and updates that reflect the latest developments in research. The topics covered are diverse, ranging from Fourier transforms to Poisson summation formulas, as well as applications in crystallography and number theory.