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Tensor algebras and harmonic analysis

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References

  1. Schwartz, L. (Séminaire), Produits tensoriels topologiques d'espaces vectoriels topologiques. Espaces vectoriels topologiques nucléaires. Applications. (1953–1954), Faculté des Sciences de Paris. (Especially numbers 1 to 8.)

  2. Naimark, M.,Normed rings. Groningen (1959). (Especially Chapter III and in particular § 15.)

  3. Mallios, A., Tensor products and harmonic analysis.Math. Ann., 158 (1965), 46–54.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bourbaki, N.,Topologie générale, Ch. 9; § 6; No. 6, 7. Hermann, Paris; A.S.I. 1045, Nouvelle édition.

  5. Rudin, W.,Fourier analysis on groups. Interscience No. 12. (Especially Ch. 5, §§ 1, 2, 6, 7.)

  6. Kurosh, A. G.,The theory of groups (translated in English). Chelsea, 1955. Vol. 1, § 24.

  7. Zygmund, A.,Trigonometric series. Vol. 1. Cambridge U. P., 1959.

  8. Zygmund, A.,Trigonometric series, p. 70; example 2.

  9. Zygmund, A.,Trigonometris series, Ch. VI; Theorem 3.6.

  10. Zygmund, A.,Trigonometric series, Ch. V; Theorem 4.2.

  11. Morse, M., Bimeasures and their integral extensions.Ann. Mat. Pura Appl., (4) 39 (1955), 345–356.

    MATH  MathSciNet  Google Scholar 

  12. Kahane, J.-P. & Salem, R.,Ensembles parfaits et séries trigonométriques. Hermann, Paris; A.S.I. 1301. Especially:

  13. Kahane, J.-P. & Salem, R.,Ensembles parfaits et s'eries trigonométriques. Hermann, Paris; A.S.I. 1301. Appendice II.

  14. Kahane, J.-P. & Salem, R.,Ensembles parfaits et s'eries trigonométriques. Hermann, Paris; A.S.I. 1301. Ch. XI, No. 6.

  15. Kahane, J.-P. & Salem, R.,Ensembles parfaits et séries trigonométriques. Hermann, Paris; A.S.I. 1301. Ch. IX, No. 6.

  16. Loève, M.,Probability theory. Van Nostrand, 1955, Ch. VI.

  17. Schwartz, L., Sur une propriété de synthèse spectrale dans les groupes non compactsC. R. Acad. Sci. Paris, 227 (1948), 424–426.

    MATH  MathSciNet  Google Scholar 

  18. Varopoulos, N. Th., Sur les ensembles parfaits et les séries trigonométriques etc.C. R. Acad. Sci. Paris, 260 (1965), 3831–3834. (We show there that every Kronecker set is a set of spectral synthesis.)

    MATH  MathSciNet  Google Scholar 

  19. .C. R. Acad. Sci. Paris, 260 (1965), 4668–4670; 5165–5168; 5997–6000. (The main ideas appear in these notes.)

    MATH  Google Scholar 

  20. Varopoulos, N. Th., Sur les ensembles parfaits et les séries trigonométriques etc.C. R. Acad. Sci. Paris, 262 (A), 384–387; 447–449; 263(A), 785–787, 834–836. (More results are given in these notes.)

  21. Herz, C. S., Sur la note précédente de M. Varopoulos.C. R. Acad. Sci. Paris, 260 (1965), 6001–6004.

    MATH  MathSciNet  Google Scholar 

  22. ,Math. Reviews, 31 (1966), 2567.

    Google Scholar 

  23. Reiter, H. J., Contributions to harmonic analysis IV.Math. Ann., 135 (1958), 467–476.

    Article  MATH  MathSciNet  Google Scholar 

  24. Gatesoupe, M.,Sur les fonctions radiales. To appear.

  25. Bochner, S. & Chandrasekharan, K.,Fourier transforms. Princeton U.P. (1949), Ch. II § 7.

  26. Courant, R. & Hilbert, D.,Methods of mathematical physics. Interscience (1953), Vol. I, Ch. VII, No. 7.

  27. Varopoulos, N. Th., Spectral synthesis on spheres.Proc. Cambridge Philos. Soc., 62 (1966), 379–387.

    Article  MathSciNet  Google Scholar 

  28. Malliavin, P., Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts.Inst. Hautes Études Sci. Publ. Math., 1959, 85–92.

  29. Malliavin, P., Ensembles de résolution spectrale.Proc. I.C.M. Stockholm, 1963, 368–378.

  30. —, Calcul symboluque et sous-algèbres deL 1(G).Bull. Soc. Math. France, 87 (1959), 181–190.

    MATH  MathSciNet  Google Scholar 

  31. Mandelbrojt, S.,Séries adhérentes, régularisation des suites, applications. Gauthier-Villars, Paris (1952) (Ch. IV).

    MATH  Google Scholar 

  32. Rudin, W., Division in algebras of infinitely differentiable functions.J. Math. Mech., 11 (1962), 797–809.

    MATH  MathSciNet  Google Scholar 

  33. Katznelson, Y., Sur le calcul symbolique dans quelques algèbres de Banach.Ann. Sci. École Norm. Sup., 76 (1959), 83–124.

    MATH  MathSciNet  Google Scholar 

  34. Kahane, J.-P. &Katznelson, Y., Contribution à deux problèmes concernant les fonctions de la classe A.Israel J. Math., 1 (1963), 110–131.

    MathSciNet  MATH  Google Scholar 

  35. Kahane, J.-P., Sur le théorème de Beurling-Pollard.Math. Scand., 20 (1967).

  36. Herz, C. S., The spectral theory of bounded functions.Trans. Amer. Math. Soc., 94 (1960), 181–232.

    Article  MATH  MathSciNet  Google Scholar 

  37. Helson, H., Kahane, J.-P., Katznelson, Y. &Rudin, W., The functions which operate on Fourier transforms.Acta Math., 102 (1959), 135–157.

    MathSciNet  MATH  Google Scholar 

  38. Kahane, J.-P., Algèbres tensorielles et analyse harmonique.Seminaire Bourbaki, May, 1965.

  39. Varopoulos, N. Th.,Summer school on topological algebra theory; September 6–16, 1966, Bruges; Presses Universitaires de Bruxelles.

    Google Scholar 

  40. Kahane, J.-P., Sur la synthèse harmonique dansl An. Acad. Brasil Ci., 32 (1960), 179–189.

    MATH  MathSciNet  Google Scholar 

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Varopoulos, N.T. Tensor algebras and harmonic analysis. Acta Math. 119, 51–112 (1967). https://doi.org/10.1007/BF02392079

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