On Alpert multiwavelets Articles uri icon

publication date

  • June 2015

start page

  • 2479

end page

  • 2494

issue

  • 6

volume

  • 143

international standard serial number (ISSN)

  • 0002-9939

electronic international standard serial number (EISSN)

  • 1088-6826

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.

keywords

  • multiwavelets; hypergeometric functions; generalized eigenvalue problem