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Umkehrformeln für Fourier-Transformationen, Approximations- und Interpolationstheorie

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Zusammenfassung

Eine formale Einsicht in die Fragen, die hier behandelt werden, erhält man wie folgt: Sei T irgendeine lineare Transformation eines Raumes E in einem Raum F, und es sei eine Umkehrformel für T von der Form

$$f = \mathop {\lim }\limits_\lambda {K_\lambda }g,$$

wenn g = Tf, gegeben.

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Literatur

  1. Butzer, P.L.: Fourier transform methods in the theory of approximation. Archiv for Rat. Mech. and Math. 5 (1960), 390–415.

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  2. Cramer, H.: On the representation of a function by certain Fourier integrals. Trans. Amer. Math. Soc. 46 (1939), 191–201.

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  3. Rooney, P.G.: On the representation of functions as Fourier transforms. Canad. Math. J. 11 (1959), 168–174.

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  4. Rooney, P.G.: On the representation of sequences as Fourier coefficients. Proc. Amer. Math. Soc. 11 (1960), 762–768.

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  5. Titchmarsh, E.C.: Theory of Fourier Integrals. (Oxford, 1937).

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  6. Zygmund, A.: Trigonometric Series, 2nd ed. (Cambridge, 1959).

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P. L. Butzer J. Korevaar

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© 1964 Springer Basel AG

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Cooper, J.L.B. (1964). Umkehrformeln für Fourier-Transformationen, Approximations- und Interpolationstheorie. In: Butzer, P.L., Korevaar, J. (eds) On Approximation Theory / Über Approximationstheorie. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Nummerischen Mathematik / Série Internationale D’Analyse Numérique, vol 5 . Springer, Basel. https://doi.org/10.1007/978-3-0348-4131-3_7

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  • DOI: https://doi.org/10.1007/978-3-0348-4131-3_7

  • Publisher Name: Springer, Basel

  • Print ISBN: 978-3-0348-4058-3

  • Online ISBN: 978-3-0348-4131-3

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