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Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications |
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| Authors: | Bradley Currey Azita Mayeli Vignon Oussa |
| Institution: | 1. Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO, 63103, USA 2. Department of Mathematics and Computer Science, City University of New York, Queensborough, New York, NY, 11364, USA 3. Department of Mathematics, Bridgewater State University, Bridgewater, MA, 02325, USA |
| 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. |
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