 Fractional and complex pseudo-splines and the construction of Parseval framesPeter Massopust, Brigitte Forster and Ole Christensen Applied Mathematics and Computation, 2017, vol. 314, issue C, 12-24 Abstract: Pseudo-splines of integer order (m, ℓ) were introduced by Daubechies, Han, Ron, and Shen as a family which allows interpolation between the classical B-splines and the Daubechies’ scaling functions. The purpose of this paper is to generalize the pseudo-splines to fractional and complex orders (z, ℓ) with α ≔ Re z ≥ 1. This allows increased flexibility in regard to smoothness: instead of working with a discrete family of functions from Cm, m∈N0, one uses a continuous family of functions belonging to the Hölder spaces Cα−1. The presence of the imaginary part of z allows for direct utilization in complex transform techniques for signal and image analyses. We also show that in analogue to the integer case, the generalized pseudo-splines lead to constructions of Parseval wavelet frames via the unitary extension principle. The regularity and approximation order of this new class of generalized splines is also discussed. Keywords: Pseudo-splines; Fractional and complex B-splines; Framelets; Filters; Parseval frames; Unitary extension principle (UEP) (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:314:y:2017:i:c:p:12-24 DOI: 10.1016/j.amc.2017.06.023 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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