TY - JOUR
T1 - Improved bounds for Laue's constant and multivariate extensions
AU - Dreier, Ilona
AU - Ehm, Werner
AU - Gneiting, Tilmann
AU - Richards, Donald
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
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U2 - 10.1002/1522-2616(200108)228:1<109::AID-MANA109>3.0.CO;2-V
DO - 10.1002/1522-2616(200108)228:1<109::AID-MANA109>3.0.CO;2-V
M3 - Article
AN - SCOPUS:0039251971
SN - 0025-584X
VL - 228
SP - 109
EP - 122
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
ER -