Document Zbl 1490.65024

Factorization of Hermite subdivision operators from polynomial over-reproduction. (English) Zbl 1490.65024

J. Approx. Theory 271, Article ID 105645, 16 p. (2021).

Summary: We study the case of Hermite subdivision operators satisfying a spectral condition of order greater than their size. We show that this can be characterized by operator factorizations involving Taylor operators and difference factorizations of a rank one vector scheme. Giving explicit expressions for the factorization operators, we put into evidence that the factorization only depends on the order of the spectral condition but not on the polynomials that define it. We further show that the derivation of these operators is based on an interplay between Stirling numbers and \(p\)-Cauchy numbers (or generalized Gregory coefficients).

Cited in 3 Documents

MSC:

65D15	Algorithms for approximation of functions
41A58	Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
11B73	Bell and Stirling numbers

Keywords:

Hermite subdivision schemes; operator factorization; \(p\)-Cauchy numbers

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References:

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