期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 484, 期 1, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2019.123713
关键词
Refinable functions; Interpolation; Univariate subdivision; General arity; Dual schemes
资金
- Research ITalian network on Approximation (RITA)
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. (C) 2019 Elsevier Inc. All rights reserved.
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