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On Alpert multiwavelets


Authors: Jeffrey S. Geronimo and Francisco Marcellán
Journal: Proc. Amer. Math. Soc. 143 (2015), 2479-2494
MSC (2010): Primary 42C40, 41A15, 33C50
DOI: https://doi.org/10.1090/S0002-9939-2015-12493-8
Published electronically: February 16, 2015
MathSciNet review: 3326030
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Abstract: The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized eigenvalue equations as well as partial difference equations. The matrix coefficients in the wavelet equation are also considered and conditions are given to obtain a unique solution.


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Additional Information

Jeffrey S. Geronimo
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332–0160

Francisco Marcellán
Affiliation: Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911, Leganés, Spain

DOI: https://doi.org/10.1090/S0002-9939-2015-12493-8
Keywords: Multiwavelets, hypergeometric functions, generalized eigenvalue problem
Received by editor(s): August 14, 2013
Received by editor(s) in revised form: January 8, 2014
Published electronically: February 16, 2015
Additional Notes: The first author was supported in part by a Simons Foundation Grant
The second author was supported by grant MTM2012-36732-C03-01 from the Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain.
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society