On Alpert multiwavelets

Geronimo, Jeffrey; Marcellán, Francisco

doi:10.1090/S0002-9939-2015-12493-8

On Alpert multiwavelets
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by Jeffrey S. Geronimo and Francisco Marcellán PDF

Proc. Amer. Math. Soc. 143 (2015), 2479-2494 Request permission

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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