Approximation of Gaussian by Scaling Functions and Biorthogonal Scaling Polynomials
Bulletin of the Malaysian Mathematical Society, Tome 32 (2009) no. 3
Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website
The derivatives of the Gaussian function, , produce the Hermite polynomials by the relation, , where , are Hermite polynomials of degree . The orthonormal property of the Hermite polynomials, , can be considered as a biorthogonal relation between the derivatives of the Gaussian, , 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.
Classification :
41A15, 41A30, 42C05, 42C15.
@article{BMMS_2009_32_3_a0,
author = {S. L. Lee},
title = {Approximation of {Gaussian} by {Scaling} {Functions} and {Biorthogonal} {Scaling} {Polynomials}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2009},
volume = {32},
number = {3},
url = {http://geodesic.mathdoc.fr/item/BMMS_2009_32_3_a0/}
}
S. L. Lee. Approximation of Gaussian by Scaling Functions and Biorthogonal Scaling Polynomials. Bulletin of the Malaysian Mathematical Society, Tome 32 (2009) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2009_32_3_a0/