Get Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, PDF

By Audrey Terras

This textual content is an creation to harmonic research on symmetric areas, targeting complex themes corresponding to larger rank areas, confident convinced matrix house and generalizations. it truly is meant for starting graduate scholars in arithmetic or researchers in physics or engineering. As with the introductory e-book entitled "Harmonic research on Symmetric areas - Euclidean area, the sector, and the Poincaré top part airplane, the fashion is casual with an emphasis on motivation, concrete examples, historical past, and functions. The symmetric areas thought of listed here are quotients X=G/K, the place G is a non-compact genuine Lie crew, corresponding to the overall linear workforce GL(n,P) of all n x n non-singular actual matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. different examples are Siegel's top part "plane" and the quaternionic higher part "plane". in relation to the overall linear team, you can still determine X with the gap Pn of n x n confident yes symmetric matrices.

Many corrections and updates were included during this new version. Updates comprise discussions of random matrix idea and quantum chaos, in addition to contemporary learn on modular varieties and their corresponding L-functions in greater rank.  Many functions were additional, reminiscent of the answer of the warmth equation on Pn, the principal restrict theorem of Donald St.

P. Richards for Pn, effects on densest lattice packing of spheres in Euclidean house, and GL(n)-analogs of the Weyl legislation for eigenvalues of the Laplacian in aircraft domains.

Topics featured during the textual content comprise inversion formulation for Fourier transforms, crucial restrict theorems, basic domain names in X for discrete teams Γ (such because the modular team GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the matter of discovering densest lattice packings of spheres in Euclidean area, automorphic kinds, Hecke operators, L-functions, and the Selberg hint formulation and its functions in spectral idea in addition to quantity theory.

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Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations by Audrey Terras

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