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An elementary construction of periodic singular integrals achieving the order of best approximation

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6. References

  1. N. I. Achieser: Vorlesungen über Approximationstheorie. Berlin 19622, xiii + 412 pp.

  2. N. K. Bary: A Treatise on Trigonometric Series, II. Oxford etc. 1964, xix + 508 pp.

  3. G. Bleimann and E. L. Stark: The fine structure of periodic approximate identities. In: Proceedings of the Colloquium on Fourier Analysis and Approximation Theory, Budapest, 16. - 21.8.1976; in print.

  4. P. L. Butzer and R. J. Nessel: Fourier Analysis and Approximation, I, New York — Basel etc. 1971, xvi + 553 pp.

  5. P. L. Butzer, R. J. Nessel, and W. Trebels: On summation processes of Fourier expansions in Banach spaces II. Saturation theorems. Tôhoku Math. J. (2) 24 (1972) 551-569.

  6. C. De La VallÉe Poussin: Leçons sur L’Approximation des Fonctions d’une Variable Reelle. Paris 1952 (19191), vi+ 151 pp.; reprinted in L’Approximation by S. Bernstein-C. de La Vallée Poussin, New York 1970, xiii + 204 pp., vii+150 pp.

  7. R. A. DeVore: The Approximation of Continuous Functions by Positive Linear Operators. Lecture Notes Math. 293 (1972) viii+289 pp.

  8. I. P. Natanson: Konstruktive Funktionentheorie. Berlin 1955, xiv+515 pp.

  9. R. J. Nessel and G. Wilmes: On Nikolskii-type inequalities for orthogonal expansions. In: Approximation Theory, II (Proc. Internat. Symp. Austin, Texas, 18.-21.1.1976; Eds. G. G. Lorentz, C. K. Chui, and L. L. Schumaker) New York etc. 1976, xi + 588 pp.; pp 479-484.

  10. E. L. Stark: Erzeugung und strukturelle Verknüpfungen von Kernen singulärer Faltungsintegrale. In: Approximation Theory, Bonn 1976 (Proc. Internat. Coll., Bonn, 8. -11.6.1976; Eds. R. Schaback and K. Scherer) Lecture Notes Math. 556 (1976) vii+466 pp.; pp. 390-402.

  11. A. F. Timan: Theory of Approximation of Functions of a Real Variable. Oxford etc. 1963, xii+631 pp.

  12. W. Trebels: Multipliers for (C, α)-Bounded Fourier Expansions in Banach Spaces and Approximation Theory. Lecture Notes Math. 329 (1973) viii+103 pp.

  13. A. H. Tureckiĭ: Saturation classes in the space C (Russ.). Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961) 411–442.

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  14. G. Wilmes: Ungleichungen vom Nikolskii- und Riesz-Typ in Banach Räumen und ihre Anwendung auf klassische Potentialräume. Dissertation, RWTH Aachen 1977, iii+132 pp.

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  1. Rheinische-Westfälische Technische Hochschule Aachen Lehrstuhl A für Mathematik, Templergraben 55, D 5100, Aachen, Bundesrepublik Deutschland

    G. Bleimann & E. L. Stark

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  1. G. Bleimann
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  2. E. L. Stark
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Bleimann, G., Stark, E.L. An elementary construction of periodic singular integrals achieving the order of best approximation. Results. Math. 2, 17–29 (1979). https://doi.org/10.1007/BF03322942

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