منابع مشابه
A note on "Positive time-frequency distributions"
—We discuss the performance of certain recently proposed positive time-frequency distribution functions with correct marginals. It turns out that for signals of the FM type, satisfactory results can only be obtained with a strongly signal dependent choice of the param eters in these distribution functions.
متن کاملA Note on Positive Definite Norm Dependent Functions
Let K be an origin symmetric star body in R. We prove, under very mild conditions on the function f : [0,∞) → R, that if the function f(‖x‖K) is positive definite on R , then the space (R, ‖ · ‖K) embeds isometrically in L0. This generalizes the solution to Schoenberg’s problem and leads to progress in characterization of n-dimensional versions, i.e. random vectors X = (X1, ...,Xn) in R n such ...
متن کاملPositive definite distributions and normed spaces
We answer a question of Alex Koldobsky. We show that for each −∞< p < 2 and each n 3−p there is a normed space X of dimension n which embeds in Ls if and only if −n < s p. © 2011 Elsevier Inc. All rights reserved. MSC: 52A21
متن کاملGeometric optimisation on positive definite matrices for elliptically contoured distributions
Hermitian positive definite (hpd) matrices recur throughout machine learning, statistics, and optimisation. This paper develops (conic) geometric optimisation on the cone of hpd matrices, which allows us to globally optimise a large class of nonconvex functions of hpd matrices. Specifically, we first use the Riemannian manifold structure of the hpd cone for studying functions that are nonconvex...
متن کاملIntegral Representations of Positive Definite Matrix-valued Distributions on Cylinders
The notion of a <7-continuous matrix-valued positive definite distribution on 5/v(2a) x RM x G is introduced, where G is an abelian separable locally compact group and where Sp/(2a) is an open ball around zero in RA' with radius la > 0 . This notion generalizes that one of strongly continuous positive definite operator-valued functions. For these objects, a Bochner-type theorem gives a suitable...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2013
ISSN: 0019-3577
DOI: 10.1016/j.indag.2013.01.008