Alpert Multiwavelets and Legendre--Angelesco Multiple Orthogonal Polynomials
Copyright policy )Alpert Multiwavelets and Legendre--Angelesco Multiple Orthogonal Polynomials
We show that the multiwavelets, introduced by Alpert in 1993, are related to type I Legendre-Angelesco multiple orthogonal polynomials. We give explicit formulas for these Legendre-Angelesco polynomials and for the Alpert multiwavelets. The multiresolution analysis can be done entirely using Legendre polynomials, and we give an algorithm, using Cholesky factorization, to compute the multiwavelets and a method, using the Jacobi matrix for Legendre polynomials, to compute the matrices in the scaling relation for any size of the multiplicity of the multiwavelets.
19 pages + 7 pages supplementary materials
FRACTAL FUNCTIONS, Mathematics, Applied, Nontrigonometric harmonic analysis involving wavelets and other special systems, Alpert multiwavelets, 0101 Pure Mathematics, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), POLYNOMIALS, 0102 Applied Mathematics, BASES, Numerical methods for wavelets, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 4901 Applied mathematics, MULTIRESOLUTION ANALYSES, Legendre-Angelesco polynomials, Science & Technology, CONSTRUCTION, Generalized hypergeometric series, \({}_pF_q\), Applied Mathematics, WAVELETS, math.CA, Mathematics - Classical Analysis and ODEs, Physical Sciences, 4904 Pure mathematics, Legendre polynomials, Mathematics, hypergeometric functions
FRACTAL FUNCTIONS, Mathematics, Applied, Nontrigonometric harmonic analysis involving wavelets and other special systems, Alpert multiwavelets, 0101 Pure Mathematics, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), POLYNOMIALS, 0102 Applied Mathematics, BASES, Numerical methods for wavelets, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 4901 Applied mathematics, MULTIRESOLUTION ANALYSES, Legendre-Angelesco polynomials, Science & Technology, CONSTRUCTION, Generalized hypergeometric series, \({}_pF_q\), Applied Mathematics, WAVELETS, math.CA, Mathematics - Classical Analysis and ODEs, Physical Sciences, 4904 Pure mathematics, Legendre polynomials, Mathematics, hypergeometric functions
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