Download E-books Harmonic Analysis on Symmetric Spaces_Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane PDF

This particular textual content is an creation to harmonic research at the least difficult symmetric areas, specifically Euclidean area, the field, and the Poincaré top part plane.  This booklet is meant for starting graduate scholars in arithmetic or researchers in physics or engineering.  Written with an off-the-cuff type, the booklet areas an emphasis on motivation, concrete examples, heritage, and, especially, purposes in arithmetic, information, physics, and engineering.

Many corrections and updates were integrated during this re-creation. Updates contain discussions of P. Sarnak and others' paintings on quantum chaos, the paintings of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's query "Can you pay attention the form of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, ultimately, the author's comparisons of continuing thought with the finite analogues.

Topics featured during the textual content contain inversion formulation for Fourier transforms, relevant restrict theorems, Poisson's summation formulation and purposes in crystallography and quantity idea, purposes of round harmonic research to the hydrogen atom, the Radon rework, non-Euclidean geometry at the Poincaré top part aircraft H or unit disc and functions to microwave engineering, basic domain names in H for discrete teams Γ, tessellations of H from such discrete staff activities, automorphic kinds, and the Selberg hint formulation and its purposes in spectral conception in addition to quantity theory.

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