Dual univariate interpolatory subdivision of every arity: Algebraic characterization and construction

A new class of univariate stationary interpolatory subdivision schemes of dual type is presented. As opposed to classical primal interpolatory schemes, these new schemes have masks with an even number of elements and are not step-wise interpolants. A complete algebraic characterization, which covers...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-04, Vol.484 (1), p.123713, Article 123713
Main Authors: Romani, Lucia, Viscardi, Alberto
Format: Article
Language:English
Subjects:
Dual schemes
General arity
Interpolation
Refinable functions
Univariate subdivision
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Summary:A new class of univariate stationary interpolatory subdivision schemes of dual type is presented. As opposed to classical primal interpolatory schemes, these new schemes have masks with an even number of elements and are not step-wise interpolants. A complete algebraic characterization, which covers every arity, is given in terms of identities of trigonometric polynomials associated to the schemes. This characterization is based on a necessary condition for refinable functions to have prescribed values at the nodes of a uniform lattice, as a consequence of the Poisson summation formula. A strategy for the construction is then showed, alongside meaningful examples for applications that have comparable or even superior properties, in terms of regularity, length of the support and/or polynomial reproduction, with respect to the primal counterparts.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123713