Abstract
As an application of the fact that the range of the wavelet transform associated to an admissible wavelet for an irreducible and square-integrable representation is a reproducing kernel Hilbert space, we give in this chapter a sampling theorem on a locally compact and Hausdorff group. This is an analogue of Shannon’s sampling theorem given in Section 2.4 of the book [7] by Blatter and Section 2.1 of the book [13] by Daubechies among others. The origin of the theorem is rooted in the papers [79, 80] by Shannon
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© 2002 Springer Basel AG
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Wong, M.W. (2002). A Sampling Theorem. In: Wavelet Transforms and Localization Operators. Operator Theory: Advances and Applications, vol 136. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8217-0_8
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DOI: https://doi.org/10.1007/978-3-0348-8217-0_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9478-4
Online ISBN: 978-3-0348-8217-0
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