Induced representations arising from a character with finite orbit in a semidirect product. (English) Zbl 1328.47077
Summary: Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from noncommutative harmonic analysis, ergodic theory, and dynamical systems. Our analysis is in the setting of semidirect products, discrete subgroups, and solenoids. Our applications include analysis and ergodic theory of Bratteli diagrams and their compact duals; of wavelet sets, and wavelet representations.
MSC:
| 47L60 | Algebras of unbounded operators; partial algebras of operators |
| 46N30 | Applications of functional analysis in probability theory and statistics |
| 46N50 | Applications of functional analysis in quantum physics |
| 42C15 | General harmonic expansions, frames |
| 65R10 | Numerical methods for integral transforms |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C75 | Structural characterization of families of graphs |
| 31C20 | Discrete potential theory |
| 46N20 | Applications of functional analysis to differential and integral equations |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 31A15 | Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
| 81S25 | Quantum stochastic calculus |
