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Band and Time Limiting, Recursion Relations and Some Nonlinear Evolution Equations

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Special Functions: Group Theoretical Aspects and Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 18))

Abstract

Let Af the Finite Fourier Transform of a function f(x) ∈ L2 (R), given by

$$\left( {Af} \right)\left(\lambda \right) = \int_{ - T}^T {{e^{i\lambda x}}} f\left( x \right)dx,\lambda \in \left[{ - \Omega ,\Omega } \right]$$

One can consider A as the result of first chopping f to the interval [-T,T], then taking its Fourier transform and then chopping again, this time to the interval [-Ω, Ω]. This explains the title of this section.

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Authors
  1. F. Alberto Grünbaum
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Editor information

Editors and Affiliations

  1. Mathematics Department, University of Wisconsin, Madison, USA

    R. A. Askey

  2. Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

    T. H. Koornwinder

  3. Department of Mathematics, University of Siegen, Germany

    W. Schempp

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© 1984 D. Reidel Publishing Company

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Grünbaum, F.A. (1984). Band and Time Limiting, Recursion Relations and Some Nonlinear Evolution Equations. In: Askey, R.A., Koornwinder, T.H., Schempp, W. (eds) Special Functions: Group Theoretical Aspects and Applications. Mathematics and Its Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9787-1_8

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  • DOI: https://doi.org/10.1007/978-94-010-9787-1_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0319-6

  • Online ISBN: 978-94-010-9787-1

  • eBook Packages: Springer Book Archive

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