Pacific Journal of Mathematics

Cantor-type uniqueness of multiple trigonometric integrals.

Victor L. Shapiro

Article information

Source
Pacific J. Math., Volume 5, Number 4 (1955), 607-622.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103044388

Mathematical Reviews number (MathSciNet)
MR0076092

Zentralblatt MATH identifier
0066.05002

Subjects
Primary: 42.2X

Citation

Shapiro, Victor L. Cantor-type uniqueness of multiple trigonometric integrals. Pacific J. Math. 5 (1955), no. 4, 607--622. https://projecteuclid.org/euclid.pjm/1103044388


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References

  • [1] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), 175-207.
  • [2] S. Bochner, Theta relations with spherical harmonics, Proc. Nat. Acad. Sci., 37 (1951), 804-808.
  • [3] S. Bochner and K. Chandrasekharan, Fourier transforms, Princeton, 1949.
  • [4] M. Brelot, Sur la structure des ensembles de capacite nulle, C. R. Acad. Sci. Paris 192 (1931), 206-208.
  • [5] M.T. Cheng, Uniqueness of multiple trigonometric series, Annals of Math. 52 (1950), 403-416.
  • [6] R. Courant and D. Hubert, Methoden der mathematischen Physik, vol. 2 Berlin, 1937.
  • [7] O. D. Kellogg, Foundation of potential theory, Berlin, 1929.
  • [8] T. Rado, Subharmonic functions,Ergebnisse der Mathematik, vol. 5, no. 1, Berlin, 1937.
  • [9] W. Rudin, Integral representations of continuous functions, Trans. Amer. Math. Soc. 68 (1950), 278-286.
  • [10] S. Saks, Theory of the integral, 2d. ed., Warsaw, 1937.
  • [11] V. L. Shapiro, An extension of results in the uniqueness theory of double trigo- nometric series, Duke Math. J. 20 (1953), 359-366.
  • [12] V. L. Shapiro, A note on the uniqueness of double trigonometric series, Proc. Amer. Math. Soc. 4 (1953), 692-695.
  • [13] MSummability and uniqueness of double trigonometric integrals, Trans. Amer. Math. Soc, 77(1954), 322-339.
  • [14] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge, 1944.
  • [15] A. Zygmund, Trigonometrical series, Warsaw, 1935.