On the mathematical properties of distributed approximating functionals

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

doi:10.1023/A:1013198218461

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 journal › Article › peer-review

6 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	83-107
Number of pages	25
Journal	Journal of Mathematical Chemistry
Volume	30
Issue number	1
DOIs	https://doi.org/10.1023/A:1013198218461
State	Published - Jul 2001

Keywords

Distributed approximating functionals (DAFs)
Gaussian function
Wavelet generator

ASJC Scopus subject areas

Chemistry(all)
Applied Mathematics

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10.1023/A:1013198218461

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abstract = "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.",

keywords = "Distributed approximating functionals (DAFs), Gaussian function, Wavelet generator",

author = "Guowei Wei and Haixiang Wang and Kouri, {Donald J.} and Manos Papadakis and Kakadiaris, {Ioannis A.} and Hoffman, {David K.}",

note = "Funding Information: ∗Research supported in part under National Science Foundation Grant CHE-0074311 and R.A. Welch Foundation Grant E-0608. ∗∗Research supported by a New Faculty Research Award of the University of Houston. ∗∗∗ The Ames Laboratory is operated for the Department of Energy by Iowa State University under Contract No. 2-7405-ENG82.",

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AU - Hoffman, David K.

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On the mathematical properties of distributed approximating functionals

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