Full rank positive matrix symbols: interpolation and orthogonality |
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| Authors: | C Conti M Cotronei T Sauer |
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| Institution: | 1.Dipartimento di Energetica “Sergio Stecco”,Università di Firenze,Firenze,Italy;2.DIMET – Dipartimento di Informatica, Matematica, Elettronica e Trasporti,Università degli Studi “Mediterranea” di Reggio Calabria,Reggio Calabria,Italy;3.Lehrstuhl für Numerische Mathematik,Justus-Liebig-Universit?t Gie?en,Gie?en,Germany |
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| Abstract: | We investigate full rank interpolatory vector subdivision schemes whose masks are positive definite on the unit circle except
the point z=1. Such masks are known to give rise to convergent schemes with a cardinal limit function in the scalar case.
In the full rank vector case, we show that there also exists a cardinal refinable function based on this mask, however, with
respect to a different notion of refinability which nevertheless also leads to an iterative scheme for the computation of
vector fields. Moreover, we show the existence of orthogonal scaling functions for multichannel wavelets and give a constructive
method to obtain these scaling functions.
AMS subject classification (2000) 42C40, 65T60, 65D05 |
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| Keywords: | subdivision schemes refinement equation full rank schemes interpolatory matrix refinable function matrix spectral factorization |
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