• Title/Summary/Keyword: Refinable function

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SYMMETRIC INTERPOLATING REFINABLE FUNCTION VECTORS

  • Kwon, Soon-Geol
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.495-503
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    • 2007
  • Symmetric interpolating refinable function vectors with compact support are of interest in several applications such as signal processing, image processing and computer graphics. It is known in [13] that orthogonal interpolating refinable function vectors can not be symmetric for multiplicity r = 2 and dilation d = 2. In this paper, we shall investigate symmetric interpolating refinable function vectors with compact support for multiplicity r = 2 and dilation d = 2 by omitting orthogonality. To illustrate our theorems and results in this paper, we shall also present some examples of symmetric interpolating refinable function vectors with compact support and high order of sum rules.

ON THE ASYMPTOTIC CONVERGENCE OF ORTHONORMAL CARDINAL REFINABLE FUNCTIONS

  • Kim, Rae-Young
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.3
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    • pp.133-137
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    • 2008
  • We prove an extended version of asymptotic behavior of the orthonormal cardinal refinable functions from Blaschke products introduced by Contronei et al [2]. In fact, we show the orthonormal cardinal refinable function ${\varphi}_{k,q}$ converges in $L^p(\mathbb{R})$ ($2{\leq}p{\leq}{\infty}$) to the Shannon refinable function as ${\kappa}{\rightarrow}{\infty}$ uniforml on a class $\mathcal{Q}_{A,B}$ of real symmetric polynomials determined by positive constants $A{\leq}B$.

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ORTHOGONAL TWO-DIRECTION REFINABLE FUNCTION OF ORDER 3

  • KWON, SOON-GEOL
    • Journal of applied mathematics & informatics
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    • v.37 no.3_4
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    • pp.307-315
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    • 2019
  • In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.