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The generalized Shannon system in wavelet space

Published online by Cambridge University Press:  17 February 2009

Hong Oh Kim  and
Jong Ha Park
Hong Oh Kim
Affiliation:
Department of Mathematics, KAIST, Kusong Dong 373–1, Yusong-Gu, Taejon 305–701, Korea.
Jong Ha Park
Affiliation:
Department of Mathematics, KAIST, Kusong Dong 373–1, Yusong-Gu, Taejon 305–701, Korea.
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Abstract

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The Shannon system is generalized and the expansion of a function in the generalized Shannon system is considered. No study of a wavelet expansion exists without the assumption of ‘fast’ decay of wavelets. The wavelet ψ which is associated with the generalized Shannon system has a ‘slow’ decay. The expansion of a function in the system is shown to converge at a point which satisfies the Lipschitz condition of order α > 0. On the other hand, there is a continuous function whose wavelet expansion in the generalized Shannon system diverges. An observation of Gibbs' phenomenon is also given.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 3 , January 2000 , pp. 386 - 400
Copyright
Copyright © Australian Mathematical Society 2000

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