Journal of Fourier Analysis and Applications

, Volume 20, Issue 2, pp 384–400 | Cite as

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

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.

Keywords

Nilpotent Lie groups Shift-invariant subspaces Frame and Reisz bases 

Mathematics Subject Classification

43 46 41 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceSaint Louis UniversitySt. LouisUSA
  2. 2.Department of Mathematics and Computer ScienceCity University of New York, QueensboroughNew YorkUSA
  3. 3.Department of MathematicsBridgewater State UniversityBridgewaterUSA

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