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Orthonormal bases generated by Cuntz algebras |
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| Authors: | Dorin Ervin Dutkay Gabriel Picioroaga Myung-Sin Song |
| Institution: | 1. University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., P.O. Box 161364, Orlando, FL 32816-1364, USA;2. University of South Dakota, Department of Mathematical Sciences, 414 E. Clark St., Vermillion, SD 57069, USA;3. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Campus Box 1653, Science Building, Edwardsville, IL 62026, USA |
| Abstract: | We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set. |
| Keywords: | Cuntz algebras Fractal Fourier basis Hadamard matrix Quadrature mirror filter |
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