Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

NECESSARY CONDITION AND SUFFICIENT CONDITION FOR THE WAVELET FRAMES IN $L^2(R^n)$

  • Wu, Guochang (Department of Mathematics and Information Science, Henan University of Finance and Economics) ;
  • Zhang, Rui (Department of Mathematics and Information Science, Henan University of Finance and Economics)
  • 투고 : 2009.10.31
  • 심사 : 2010.05.26
  • 발행 : 2010.09.30
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초록

The main goal for this paper is consider the necessary conditions and sufficient conditions of wavelet frames in higher dimensions with an arbitrary expanding matrix dilation. At first, we give a necessary condition of wavelet frame in $L^2(R^n)$, which generalizes the univariate results of Shi from one dimension with an arbitrary real number a(a > 1) dilation to higher dimension with an arbitrary expansive matrix dilation. Secondly, we deduce a necessary condition for wavelet frames in $L^2(R^n)$ when the function $\psi$ satisfies some property of the decay. For the case n = 1, we obtain a corollary which has weaker condition comparing with existing result.

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참고문헌

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