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Paley-Wiener Approximations and Multiscale Approximations in Sobolev and Besov Spaces on Manifolds

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Abstract

An approximation theory by bandlimited functions (≡ Paley-Wiener functions) on Riemannian manifolds of bounded geometry is developed. Based on this theory multiscale approximations to smooth functions in Sobolev and Besov spaces on manifolds are obtained. The results have immediate applications to the filtering, denoising and approximation and compression of functions on manifolds. There exists applications to problems arising in data dimension reduction, image processing, computer graphics, visualization and learning theory.

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Authors and Affiliations

  1. Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA

    Isaac Pesenson

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  1. Isaac Pesenson
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Correspondence to Isaac Pesenson.

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Communicated by Steven Krantz.

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Pesenson, I. Paley-Wiener Approximations and Multiscale Approximations in Sobolev and Besov Spaces on Manifolds. J Geom Anal 19, 390–419 (2009). https://doi.org/10.1007/s12220-008-9059-2

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  • DOI: https://doi.org/10.1007/s12220-008-9059-2

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