Some analytical considerations on two-scale relations
(1994) Nuovo Cimento B — Vol. 109, n° 8, p. 871-890 (1994)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- Scaling functions that generate a multiresolution analysis (MRA) satisfy, among other conditions, the so-called <<two-scale relation>> (TSR). In this paper we discuss a number of properties that follow from the TSR alone, independently of any MRA: position of zeros (mainly for continuous scaling functions), existence theorems (using fixed point and eigenvalue arguments) and orthogonality relation between integer translates.
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Antoine, J.-P., & Bagarello, F. (1994). Some analytical considerations on two-scale relations. Nuovo Cimento B, 109(8), 871-890. https://hdl.handle.net/2078.5/25959 (Original work published 1994)