 A recursive procedure to obtain a class of orthogonal polynomial waveletsM. Moncayo and R.J. Yáñez Mathematics and Computers in Simulation (MATCOM), 2008, vol. 77, issue 2, 266-273 Abstract: In this paper we present a recursive approach to generate complex orthogonal polynomial systems. The systems belong to a class of polynomial wavelets successfully introduced by Skopina [M. Skopina, Orthogonal polynomial Shauder bases in C[−1,1] with optimal growth of degrees, Sb. Math. 192 (3) (2001) 433–454; M. Skopina, Multiresolution analysis of periodic functions, East J. Approx. 3 (1997) 203–224]. Consequently, by using the obtained recursive-type relation, it is possible to generate a great variety of complex polynomial functions which satisfy useful wavelet-like properties. We prove some additional multiscale results concerning these systems. More precisely, we state a practical two-scale relation and the decomposition and reconstruction formulae which determine the multiresolution analysis framework. From the reconstruction formula, we obtain the recursive approach which provides the Skopina’s systems. Finally, a numerical example in which explicit complex orthogonal polynomials are found recursively is presented. Keywords: Orthogonal polynomials; Wavelets; Multiresolution analysis; Decomposition and reconstruction formulae (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:matcom:v:77:y:2008:i:2:p:266-273 DOI: 10.1016/j.matcom.2007.08.007 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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