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Improved Bounds for Laue's Constant and Multivariate Extensions
Author(s) -
Dreier Ilona,
Ehm Werner,
Gneiting Tilmann,
Richards Donald
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200108)228:1<109::aid-mana109>3.0.co;2-v
Subject(s) - mathematics , constant (computer programming) , multivariate statistics , geometry , statistics , computer science , programming language
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 $\hat p$ , which is proportional to the characteristic function of p . The products λ( p ) = Var( p ) Var( $\hat p$ ) 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.