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QA403. FCT 96665 Excursions in harmonic analysis | QA403. FCT 96824 Excursions in harmonic analysis | QA403. FCT 96973 Pseudodifferential equations over non-archimedean spaces | QA403. FCT 97269 Harmonic analysis on symmetric spaces | QA403. FCT 97409 Extensions of positive definite functions | QA403. FCT 97480 Excursions in harmonic analysis | QA403. FCT 97786 Lecture notes on wavelet transforms |
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This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
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