• Title, Summary, Keyword: Shannon refinable function

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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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