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On some theorems of Hardy, Littlewood and Titchmarsh

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Bibliography

  1. Achieser, N.: Theory of Approximation. New York 1956, 307 pp.

  2. Bochner, S., andK. Chandrasekharan: Fourier Transforms. Princeton 1949, 219 pp.

  3. Butzer, P. L.: Über den Approximationsgrad des Identitätsoperators durch Halbgruppen von linearen Operatoren und Anwendungen auf die Theorie der singulären Integrale. Math. Ann.133, 410–425 (1957).

    Google Scholar 

  4. Butzer, P. L.: Representation and approximation of functions by general singular integrals. Nederl. Akad. Wetensch. Proc. Ser. A,63 (= Indag. Math.22) 1–24 (1960).

    Google Scholar 

  5. Butzer, P. L.: Sur le rôle de la transformation de Fourier dans quelques problèmes d'approximation. C. R. Acad. Sci. (Paris)249, 2467–2469 (1959).

    Google Scholar 

  6. Butzer, P. L.: Fourier transform methods in the theory of approximation. Arch. Rational Mech. Anal.5, 390–415 (1960).

    Google Scholar 

  7. Butzer, P. L.: On Dirichlet's Problem for the half-space and the behavior of its solution on the boundary. J. of Math. Anal. and Applications1 (1960) (in print).

  8. Butzer, P. L., andH. König: An application of Fourier-Stieltjes transforms in approximation theory. Arch. Rational Mech. Anal.5, 416–419 (1960).

    Google Scholar 

  9. Cramér, H.: On the representation of functions by certain Fourier integrals. Trans. Am. Math. Soc.46, 190–201 (1939).

    Google Scholar 

  10. Erdélyi, A. et al.: Tables of Integral Transforms. Vol. I (1954) XX + 391 pp.

  11. Hardy, G. H., andJ. E. Littlewood: Some properties of fractional integrals. Math. Z.27, 565–606 (1928).

    Google Scholar 

  12. Hardy, G. H., andJ. E. Littlewood: A convergence criterion for Fourier series. Math. Z.28, 612–634 (1928).

    Google Scholar 

  13. Hille, E., andR. S. Phillips: Functional Analysis and Semigroups. (Revised edition), XII + 808 pp. New York 1957.

  14. Titchmarsh, E. C.: A Theorem on Lebesgue integrals. J. Lond. Math. Soc.2, 36–37 (1927).

    Google Scholar 

  15. Titchmarsh, E. C.: The Theory of Functions. (Second edition), X + 454 pp. Oxford 1939.

  16. Titchmarsh, E. C.: Introduction to the Theory of Fourier Integrals. VIII + 395 pp. Oxford 1937.

  17. Widder, D. V.: The Laplace Transform. X + 406 pp. Princeton 1941.

  18. Zygmund, A.: Trigonometrical Series. Vol. I, II, (revised edition). Cambridge 1959.

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  1. Aachen

    P. L. Butzer

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Butzer, P.L. On some theorems of Hardy, Littlewood and Titchmarsh. Math. Ann. 142, 259–269 (1961). https://doi.org/10.1007/BF01353418

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