Journal d’Analyse Mathématique

, Volume 30, Issue 1, pp 131–140 | Cite as

Towards a Wiener-Lévy theorem for nuclear operators

  • James A. Cochran
Article
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Keywords

Integral Operator Fourier Coefficient Characteristic Number Absolute Convergence Closed Domain 
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References

  1. 1.
    S. Bochner,Lectures on Fourier Analysis, Princeton University, 1936–37; notes by A. A. Brown et al., Edward Bros., Ann Arbor, Michigan, 1937.Google Scholar
  2. 2.
    J. A. Cochran,Summability of singular values of L2 kernels—analogies with Fourier series, Enseignement Math. (2),22 (1976).Google Scholar
  3. 3.
    N. Dunford and J. T. Schwartz,Linear Operators, Part II, Interscience, New York, 1963.MATHGoogle Scholar
  4. 4.
    I. C. Gohberg and M. G. Krein,Introduction to the theory of linear nonselfadjoint operators. Translations of Math. Mono., vol. 18, Amer. Math. Soc, Providence, R. I., 1969.Google Scholar
  5. 5.
    A. A. Konyushkov,Best approximation by trigonometric polynomials and Fourier coefficients, Mat. Sb.44 (86) (1958), 53–84 (in Russian).MathSciNetGoogle Scholar
  6. 6.
    P. Lévy,Sur la convergence absolue des séries de Fourier, C. R. Acad. Sci. Paris196 (1933), 463–464; Compositio Math.1 (1934–35), 1–14.MATHGoogle Scholar
  7. 7.
    G. G. Lorentz,Fourier-Koeffizienten und Funktionenklassen, Math. Z.51 (1948), 135–149.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. R. McLaughlin,Absolute convergence of series of Fourier coefficients, Trans. Amer. Math. Soc.184 (1973), 291–316.CrossRefMathSciNetGoogle Scholar
  9. 9.
    F. Smithies,The eigen-values and singular values of integral equations, Proc. London Math. Soc. (2)43 (1937), 255–279.MATHGoogle Scholar
  10. 10.
    O. Szász,über den Konvergenzexponenten der Fourierschen Reihen gewisser Funktionenklassen, Sitzungsber. Akad. Wiss. München Math. Phys. Kl. (1922), 135–150; see alsoCollected Mathematical Papers, Dept. of Math., Cincinnati, Ohio, 1955, pp. 684–699.Google Scholar
  11. 11.
    O. Szász,über die Fourierschen Reihen gewisser Funktionenklassen, Math. Ann.100 (1928), 530–536; see alsoCollected Mathematical Papers, op. cit., 1955, pp. 758–764.CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    N. Wiener,Tauberian theorems, Ann. Math. (2)33 (1932), 1–100. See alsoThe Fourier Integral and Certain of its Applications, Cambridge University Press, London, 1933.MathSciNetCrossRefGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1976

Authors and Affiliations

  • James A. Cochran
    • 1
  1. 1.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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