Title

Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications

Publication Date

2014

Document Type

Article

Abstract

Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center, we use operator-valued periodization to give a range-function type characterization of shift-invariant spaces of function on the group. We then give characterizations of frame and Riesz families for shift-invariant spaces.

Original Citation

Currey, B., Mayeli, A., & Oussa, V. (2014). Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications. Journal of Fourier Analysis and Applications, 20(2), 384-400. https://doi.org/10.1007/s00041-013-9316-z