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A new approach to interpolating scaling functions |
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| Authors: | Stephan Dahlke Karlheinz Gröchenig Peter Maass |
| Institution: | 1. Institut fü Geometrie und Praktische Mathematik , Aachen, 52056, Germany;2. Department of Mathematics U–9 , University of Connecticut , Storrs, CT, 06269–3009, U.S.A;3. Fachbereich Mathematik , Universit?t Potsdam , Potsdam, 601553,14415, Germany |
| Abstract: | We present a new method to construct interpolating refinable functions in higher dimensions. The approach is based on the solutions to specific Lagrange interpolation problems by polynomials and applies to a large class of scaling matrices. The resulting scaling functions automatically satisfy certain Strang-Fix conditions. Several examples are discussed. |
| Keywords: | Interpolating scaling functions strang-fix conditions polynomial interpolation expanding scaling matrices |