On this page Definition Chapters and Articles Related Terms Recommended Publications Featured Authors Chapters and Articles You might find these chapters and articles relevant to this topic. Vector Spaces, Hilbert Spaces, and the L2 Space Don Hong, ... Robert Gardner, in Real Analysis with an Intr...
We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we propose a (re)definition of Hotelling's T that naturally expands to any separable Hilbert space that...
4.2.1. Definition. — Let X be a separable Banach space and N ⊆ X be Borel. (1) N is Haar null whenever there is a Borel probability measure µ on X such that µ(N + x) = 0 for every x ∈ X. (2) N is Aronszajn null whenever for every sequence {xi} whose span is...
then from the definition of \(\Gamma ({{\hat{\omega }}}^{k+1})\) and (29), it follows that $$\begin{aligned} dist (0, \partial \Gamma ({{\hat{\omega }}}^{k+1})) \leqslant {\mathcal {B}}_*(\Vert x^{k+1}-x_{ac}^k\Vert +\Vert \triangle y^{k+1}\Vert )...
Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f: X → ℝ be bounded and L... D Azagra,R Fry,L Keener - 《Bulletin of the London Mathematical Society》 被引量: 6发表: 2010年 加载更多来源...
Version of 26.9.16 The Lebesgue density theorem in separable metric spaces D.H.Fremlin University of Essex, Colchester, England Proposition Let X be a separable metrizable space and µ a locally finite quasi-Radon measure on X. Then there is a metric ρ on X, compatible with its topology...
We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we propose a (re)definition of Hotelling's T-2 that naturally expands to any separable Hilbert space ...
In the paper there are considered random variables, the values of which are taken from a separable HILBERT space. By introducing a scalar product one may define the correlation coefficient between such random variables and basing on this definition the maximal correlation. Using a conception ...
A frame for a separable Hilbert space H gives stable, but usually redundant, series representations of each element in the space. The best-known frames for function spaces are coherent state frames of the form {σ(x)f}x∈X where σ is a unitary representation of a locally compact group G...
The fuglede commutativity theorem modulo the hilbert-schmidt class and generating functions for matrix operators We prove the following statements about bounded linear operators on a separable, complex Hilbert space: (1) Every normal operator $N$ that is similar to a ... G Weiss - 《Transactions...