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Title: Approximation of Gaussian by scaling functions and biorthogonal scaling polynomials
Authors: Lee, S.L. 
Keywords: B-splines
Gaussian function
Hermite polynomials
Normal approximation
Scaling functions
Variation diminishing
Issue Date: 2009
Citation: Lee, S.L. (2009). Approximation of Gaussian by scaling functions and biorthogonal scaling polynomials. Bulletin of the Malaysian Mathematical Sciences Society 32 (3) : 261-282. ScholarBank@NUS Repository.
Abstract: The derivatives of the Gaussian function, produce the Hermite polynomials by the relation, (-1)mG(m)(x) = Hm(x)G(x), m=0,1,..., where Hm(x) are Hermite polynRmials of degree m.The orthonormal property of the Hermite polynomials, can be considered as a biorthogonal relation between the derivatives of the Gaussian, {(-1)nG(n): n = 0, 1,...}, and the Hermite polynomials. These relationships between the Gaussian and the Hermite polynomials are useful in linear scale-space analysis and applications to human and machine vision and image processing. The main objective of this paper is to extend these properties to a family of scaling functions that approximate the Gaussian function and to construct a family of Appell sequences of scaling biorthogonal polynomials that approximate the Hermite polynomials.
Source Title: Bulletin of the Malaysian Mathematical Sciences Society
ISSN: 01266705
Appears in Collections:Staff Publications

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