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Analysis of Divergence pp 477–512Cite as

Spline type summability for multivariate sampling

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The introductory material briefly describes certain mathematical aspects of signal processing which are centered around the celebrated Whittaker-Kotelnikov-Shannon sampling theorem and the spline type summability method for cardinal series developed by Schoenberg. The bulk of this article is devoted to an exposition of a version of the spline summability method for recovering multivariate band limited functions from discrete lattice samples which uses polyharmonic splines. The pertinent theory of such splines is outlined and the details of the reconstruction method, whose range of application includes data which may grow at infinity, are developed. Some of the proofs and results are new, even when reduced to the univariate case. Certain related material, including generalizations and numerical aspects, is also briefly discussed.

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  1. W. R. Madych
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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Maine, Orono, ME, 04469, USA

    William O. Bray

  2. Department of Mathematics and Statistics, University of Missouri, Rolla Bldg 202, Rolla, MO, 65409, USA

    Časlav V. Stanojević

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© 1999 Birkhäuser Boston

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Madych, W.R. (1999). Spline type summability for multivariate sampling. In: Bray, W.O., Stanojević, Č.V. (eds) Analysis of Divergence. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2236-1_27

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  • DOI: https://doi.org/10.1007/978-1-4612-2236-1_27

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7467-4

  • Online ISBN: 978-1-4612-2236-1

  • eBook Packages: Springer Book Archive

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