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Contractions of fourier coefficients and Fourier integrals

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References

  1. A. Beurling, On the spectral synthesis of bounded functions,Acta Math. 81 (1949), 225–238.

    Article  Google Scholar 

  2. R. P. Boas, Integrability of trigonometric series,Duke Math. Journ. 18 (1951), 787–793.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. P. Boas, Absolute convergence and integrability of trigonometric series,Journal of Rational Mechanics and Analysis, 5 (1956), 621–632.

    MathSciNet  Google Scholar 

  4. R. P. Boas, Beurling's test for absolute convergence of Fourier series,Bull. Amer. Math. Soc.,66, (1960), 24–26.

    MATH  MathSciNet  Google Scholar 

  5. R. P. Boas and S. Izumi, Absolute convergence of some trigonometric series I,Journ. Indian Math. Soc., (to appear).

  6. G. H. Hardy, The arithmetic mean of a Fourier constant,Mess. of Math.,58, (1928), 50–52.

    Google Scholar 

  7. G. H. Hardy, On a theorem of Paley and Wiener,Proc. Canbridge Phil. Soc.,33 (1937), 1–5.

    Article  MATH  Google Scholar 

  8. G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge (1934).

  9. G. H. Hardy and W. W. Rogosinski, Fourier series, Cambridge (1949).

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

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Izumi and Tsuchikura. Absolute convergence of Fourier expansions,Tohoku Math. Journ, (2), 7 (1955), 243–251.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. P. Kahane, Sur certaines classes de séries de Fourier absolument convergentes,Journ. Math. Pures Appl. (9), 35 (1956), 249–259.

    MATH  MathSciNet  Google Scholar 

  13. J. P. Kahane, Sur un problème de Littlewood,Nederl. Akad. Wetensch. Proc. Ser. A. 60—Indag. Math. 19 (1957), 268–271.

    MathSciNet  Google Scholar 

  14. A. A. Konyuskov, Best approximation by trigonometric polynomials and Fourier coefficients,Mat. Sh. N. S., 44 (86) (1958), 53–84 (Russian).

    MathSciNet  Google Scholar 

  15. R. C. A. Paley and N. Wiener, Notes on the theory and application of Fourier tansforms,Trans. Amer. Math. Soc., 35 (1933), 348–356.

    Article  MATH  MathSciNet  Google Scholar 

  16. W. Rudin, Transformations des coefficients de Fourier,C. R. Acad. Sci. Paris, 243 (1956), 638–640.

    MATH  MathSciNet  Google Scholar 

  17. A. Zygmund, Some points in the theory of trigonometric and power series,Trans. Amer. Math. Soc., 36 (1934), 586–616, specially 615–616.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. Zygmund, Trigonometric series, Cambridge (1959), vol. I and II.

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Authors and Affiliations

  1. Tokyo, Japan

    Masakiti Kinukawa

  2. Northwestern University, Evanston, Illinois, U.S.A.

    Masakiti Kinukawa

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  1. Masakiti Kinukawa
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This research was supported by the National Science Foundation (in U.S.A.)

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Kinukawa, M. Contractions of fourier coefficients and Fourier integrals. J. Anal. Math. 8, 377–406 (1960). https://doi.org/10.1007/BF02786857

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