New York Journal of Mathematics
Volume 21 (2015) 783-800


Palle Jorgensen and Feng Tian

Induced representations arising from a character with finite orbit in a semidirect product

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Published: August 24, 2015
Keywords: Hilbert space, unitary representation, induced representations, Frobenius reciprocity, semidirect products, imprimitivity, Pontryagin duality, direct integral decompositions, wavelet-sets, noncommutative harmonic analysis, Halmos-Rohlin, C*-algebra, solenoid.
Subject: Primary: 47L60, 46N30, 46N50, 42C15, 65R10, 05C50, 05C75, 31C20; Secondary: 46N20, 22E70, 31A15, 58J65, 81S25

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.

Author information

Palle Jorgensen:
Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, U.S.A.

Feng Tian:
Department of Mathematics, Trine University, IN 46703, U.S.A.