Improved bounds for Laue's constant and multivariate extensions

Ilona Dreier, Werner Ehm, Tilmann Gneiting, Donald Richards

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Denote by P the class of probability density functions on ℝ with a nonnegative and integrable characteristic function. For each p ∈ P, there exists an adjoint density p̂, which is proportional to the characteristic function of p. The products λ(p) = Var(p)Var(p̂) 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 < Λ < 0.85024. Further results and related estimates are also obtained for a multivariate version of the uncertainty relation which is based on univariate projections.

Original languageEnglish (US)
Pages (from-to)109-122
Number of pages14
JournalMathematische Nachrichten
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • General Mathematics


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