Original Paper

Improved Bounds for Laue's Constant and Multivariate Extensions

  1. Ilona Dreier 1,
  2. Werner Ehm2,
  3. Tilmann Gneiting3,
  4. Donald Richards4

Article first published online: 10 JUL 2001

DOI: 10.1002/1522-2616(200108)228:1<109::AID-MANA109>3.0.CO;2-V

Issue

Mathematische Nachrichten

Mathematische Nachrichten

Volume 228, Issue 1, pages 109–122, August 2001

Additional Information

How to Cite

Dreier , I., Ehm, W., Gneiting, T. and Richards, D. (2001), Improved Bounds for Laue's Constant and Multivariate Extensions. Mathematische Nachrichten, 228: 109–122. doi: 10.1002/1522-2616(200108)228:1<109::AID-MANA109>3.0.CO;2-V

Author Information

  1. 1

    Institut für Mathematische Stochastik, Technische Universität Dresden, Mommsenstr. 13, D-01062 Dresden, Germany

  2. 2

    Technische Universität Dresden, Mommsenstr. 13, D-01062 Dresden, Germany

  3. 3

    Department of Statistics, University of Washington, Box 354322Seattle, Washington 98195-4322, U. S. A.

  4. 4

    Division of Statistics, University of Virginia, Halsey Hall, Charlottesville, Virginia, 22903, U. S. A.

Publication History

  1. Issue published online: 10 JUL 2001
  2. Article first published online: 10 JUL 2001
  3. Manuscript Accepted: 30 JUL 1999
  4. Manuscript Received: 10 MAY 1999

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Keywords:

  • Bessel function;
  • characteristic function;
  • convolution;
  • Fourier transform;
  • isotropic;
  • Laue's constant;
  • positive-definite;
  • uncertainty principle

Abstract

Denote by �� the class of probability density functions on ℝ with a nonnegative and integrable characteristic function. For each p ∈ ��, there exists an adjoint density equation image, which is proportional to the characteristic function of p. The products λ(p) = Var(p) Var(equation image) have a greatest lower bound Λ known as Laue's constant. In this paper we improve the previous estimates of Λ, proving that 0.543 < 0.85024. Further results and related estimates are also obtained for a multivariate version of the uncertainty relation which is based on univariate projections.

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