Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials

Analysis Seminar
Wednesday, January 11, 2017 - 13:05
1 hour (actually 50 minutes)
Skiles 005
Katholieke University Lueven
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.Based on joint work with J.S. Geronimo and P. Iliev