On the mathematical properties of distributed approximating functionals

Guowei Wei, Haixiang Wang, Donald J. Kouri, Manos Papadakis, Ioannis A. Kakadiaris, David K. Hoffman

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This work investigates some mathematical properties of the Distributed Approximating Functionals (DAFs). We prove that certain classes of DAFs yield Unity Approximations. Two distinct classes which serve as examples are the Hermite-DAFs and the Sinc-class DAFs. Detailed proofs are given. A wavelet generator is constructed using the Continuous Wavelet Transform with repect to the scale parameter. Taking the Gaussian function as the scaling function, a numerical experiment is carried out demonstrating the use of the resulting wavelet for edge detection.

Original languageEnglish (US)
Pages (from-to)83-107
Number of pages25
JournalJournal of Mathematical Chemistry
Issue number1
StatePublished - Jul 2001


  • Distributed approximating functionals (DAFs)
  • Gaussian function
  • Wavelet generator

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics


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