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Coherent Frames and Irregular Sampling

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Recent Advances in Fourier Analysis and Its Applications

Part of the book series: NATO ASI Series ((ASIC,volume 315))

Abstract

It is the purpose of this short note to highlight perhaps unexpected connections between the topics described in the papers [G2] and [HW1] in this volume, and at the same time between various papers within a series of joint publications [FG1-8] with K.Groechenig on the two topics indicated in the title: Algorithms that allow to recover a function (or tempered distribution) f from a suitable family of coefficients, which arise as integrals of f against a countable coherent family of functions (such as Heisenberg or affine frames) and the problem of reconstructing a band-limited function from a (sufficiently rich) set of irregularly taken sampling values. As will be pointed out in detail below the basic observation, which may be taken as an explanation of most common results for these two settings, concerns properties of functions which arise as convolution products with nice, integrable functions on a locally compact group.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of MARYLAND, College Park 1, MD, 20742, USA

    Hans G. Feichtinger

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  1. Hans G. Feichtinger
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Editor information

Editors and Affiliations

  1. Prometheus Inc., Newport, RI, USA

    J. S. Byrnes

  2. University of Massachusetts at Boston, Boston, MA, USA

    J. S. Byrnes

  3. Harvard University, Cambridge, MA, USA

    Jennifer L. Byrnes

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© 1990 Kluwer Academic Publishers

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Feichtinger, H.G. (1990). Coherent Frames and Irregular Sampling. In: Byrnes, J.S., Byrnes, J.L. (eds) Recent Advances in Fourier Analysis and Its Applications. NATO ASI Series, vol 315. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0665-5_24

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  • DOI: https://doi.org/10.1007/978-94-009-0665-5_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6784-3

  • Online ISBN: 978-94-009-0665-5

  • eBook Packages: Springer Book Archive

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