Duke Mathematical Journal

The Beurling-Selberg extremal functions for a ball in Euclidean space

Jeffrey J. Holt and Jeffrey D. Vaaler

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 83, Number 1 (1996), 203-248.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077244253

Mathematical Reviews number (MathSciNet)
MR1388849

Zentralblatt MATH identifier
0859.30029

Digital Object Identifier
doi:10.1215/S0012-7094-96-08309-X

Subjects
Primary: 30D20: Entire functions, general theory
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Citation

Holt, Jeffrey J.; Vaaler, Jeffrey D. The Beurling-Selberg extremal functions for a ball in Euclidean space. Duke Math. J. 83 (1996), no. 1, 203--248. doi:10.1215/S0012-7094-96-08309-X. http://projecteuclid.org/euclid.dmj/1077244253.


Export citation

References

  • [1] R. P. Boas, Entire Functions, Academic Press, New York, 1954.
  • [2] L. de Branges, Hilbert Spaces of Entire Functions, Prentice-Hall, Englewood Cliffs, N.J., 1968.
  • [3] L. de Branges, Homogeneous and periodic spaces of entire functions, Duke Math. J. 29 (1962), 203–224.
  • [4] H. Dym, An introduction to de Branges spaces of entire functions with applications to differential equations of the Sturm-Liouville type, Advances in Math. 5 (1970), 395–471.
  • [5] S. W. Graham and J. D. Vaaler, A class of extremal functions for the Fourier Transform, Trans. Amer. Math. Soc. 265 (1981), no. 1, 283–302.
  • [6] S. W. Graham and J. D. Vaaler, Extremal functions for the Fourier Transform and the large sieve, Topics in Classical Number Theory (Budapest, 1981) ed. G. Halász, Colloq. Math. Soc. János Bolyai, vol. 34, North-Holland, Amsterdam, 1984, pp. 599–615.
  • [7] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1967.
  • [8] I. I. Hirschman and D. V. Widder, The Convolution Transform, Princeton Univ. Press, Princeton, 1955.
  • [9] M. Krein, A contribution to the theory of entire functions of exponential type, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 11 (1947), 309–326.
  • [10] E. Laguerre, Sur les fonctions du genre zéro et du genre un, C. R. Acad. Sci. Paris Sér. I Math. 98 (1882), 828–831.
  • [11] R. G. Laha and V. K. Rohatgi, Probability Theory, Wiley, New York, 1979.
  • [12] H. L. Montgomery, The analytic principle of the large sieve, Bull. Amer. Math. Soc. 84 (1978), no. 4, 547–567.
  • [13] H. L. Montgomery and J. D. Vaaler, Maximal variants of basic inequalities, Proceedings of the Congress on Number Theory (Spanish) (Zarauz, 1984), Univ. País Vasco-Euskal Herriko Unib., Bilbao, 1989, pp. 181–197.
  • [14] H. L. Montgomery and R. C. Vaughan, The large sieve, Mathematika 20 (1973), 119–134.
  • [15] H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. (2) 8 (1974), 73–82.
  • [16] G. Pólya, Über Annäherung durch Polynome mit lauter reelen Wurzeln, Rend. Circ. Mat. Palermo 36 (1913), 279–295.
  • [17] A. Selberg, Remarks on sieves, Proceedings of the 1972 Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972), University of Colorado, Boulder, 1972, pp. 205–216.
  • [18] A. Selberg, Lectures on Sieves, Atle Selberg: Collected Papers, Vol. II, Springer-Verlag, Berlin, 1991, pp. 65–247.
  • [19] E. M. Stein, Functions of exponential type, Ann. of Math. (2) 65 (1957), 582–592.
  • [20] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
  • [21] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 183–216.