Group Representations and Non-commutative Harmonic Analysis with Applications to Analysis, Number Theory, and Physics |
Contents
Some Examples of Gspaces | 6 |
4 | 22 |
Preliminaries Concerning Infinite Groups | 38 |
8 other sections not shown
Common terms and phrases
action of G additive group algebraic number field analogue analytic automorphism Borel function Borel sets Borel subset chaos character closed subgroup compact commutative group decomposition defined denote direct product direct sum disjoint elements equations equivalence class ergodic action ergodic theory exist finite dimensional follows Fourier transform G-space given group G group representations H₁ Haar measure Hilbert space homomorphism identity infinite integers intertwining operator invariant measure invariant measure class invariant subspace irreducible representations irreducible unitary representations isomorphic Let G locally compact commutative locally compact group mapping modular forms momentum observables Moreover multiplicity free notion number theory obtain one-dimensional orbit particle primary representations problem projection valued measure quadratic forms quantization quantum mechanics quotient random variables real line real numbers regular representation representation of G sample function semi-direct product sense separable locally compact spectrum strictly ergodic subrepresentation system of imprimitivity theorem topology unique unitary representation vector space velocity zero