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Uncertainty products of local periodic wavelets

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Abstract

This paper is on the angle–frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration, scaling functions and wavelets associated with a family of generalized periodic splines are studied. This family is generated by periodic weighted convolutions, and it includes the well‐known periodic B‐splines and trigonometric B‐splines.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260, Republic of Singapore

    Say Song Goh & Chee Heng Yeo

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  1. Say Song Goh
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  2. Chee Heng Yeo
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Goh, S.S., Yeo, C.H. Uncertainty products of local periodic wavelets. Advances in Computational Mathematics 13, 319–333 (2000). https://doi.org/10.1023/A:1018962428951

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