Search results for "Linear subspace"
showing 10 items of 65 documents
*-Representations, seminorms and structure properties of normed quasi*-algebras
2008
The class of -representations of a normed quasi -algebra (X;A0) is in- vestigated, mainly for its relationship with the structure of (X;A0). The starting point of this analysis is the construction of GNS-like -representations of a quasi -algebra (X;A0) dened by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms denes some seminorms (in some cases, C -seminorms) that provide useful information on the structure of (X;A0) and on the continuity properties of its -representations. 1. Introduction. A quasi -algebra is a couple (X;A0), where X is a vector space with involution , A0 is a -algebra and a vector subspace of X, and X is an A0-bimodule who…
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces
2007
We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak ∗ separable admits a closed linear subspace whose dual is not weak ∗ -separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2homogeneous polynomials.
On the conical density properties of measures on $\mathbb{R}^n$
2005
We compare conical density properties and spherical density properties for general Borel measures on $\mathbb{R}^n$ . As a consequence, we obtain results for packing and Hausdorff measures $\mathcal{P}_h$ and $\mathcal{H}_h$ provided that the gauge function $h$ satisfies certain conditions. One consequence of our general results is the following: let $m, n\,{\in}\,\mathbb{N}, 0\,{\lt}\,s\,{\lt}\,m\,{\leq}\,n$ , $0\,{\lt}\,\eta\,{\lt}\,1$ , and suppose that $V$ is an $m$ -dimensional linear subspace of $\mathbb{R}^n$ . Let $\mu$ be either the $s$ -dimensional Hausdorff measure or the $s$ -dimensional packing measure restricted to a set $A$ with $\mu(A)\,{\lt}\,\infty$ . Then for $\mu$ -almos…
Complemented Subspaces and Interpolation Properties in Spaces of Polynomials
1997
LetXbe a Banach space whose dualX* has typep ∈ (1, 2]. Ifmis an integer greater thanp/(p − 1) and (xn) is a seminormalized sequence weakly convergent to zero, there is a subsequence (yn) of (xn) such that, for each element (an) ofl∞, there is anm-homogeneous continuous polynomialPonXwithP(yn) = an,n = 1, 2,… . Some interpolation and complementation properties are also given in P(mlp), form < p, as well as in other spaces of polynomials and multilinear functionals.
Efficient and Long-Lived Field-Free Orientation of Molecules by a Single Hybrid Short Pulse
2005
We show that a combination of a half-cycle pulse and a short nonresonant laser pulse produces a strongly enhanced postpulse orientation. Robust transients that display both efficient and long-lived orientation are obtained. The mechanism is analyzed in terms of optimal oriented target states in finite Hilbert subspaces and shows that hybrid pulses can prove useful for other control issues.
Generalized Riesz systems and quasi bases in Hilbert space
2019
The purpose of this article is twofold. First of all, the notion of $(D, E)$-quasi basis is introduced for a pair $(D, E)$ of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ such that $\sum_{n=0}^\infty \ip{x}{\varphi_n}\ip{\psi_n}{y}=\ip{x}{y}$ for all $x \in D$ and $y \in E$. Secondly, it is shown that if biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ form a $(D ,E)$-quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators.
An overview of incremental feature extraction methods based on linear subspaces
2018
Abstract With the massive explosion of machine learning in our day-to-day life, incremental and adaptive learning has become a major topic, crucial to keep up-to-date and improve classification models and their corresponding feature extraction processes. This paper presents a categorized overview of incremental feature extraction based on linear subspace methods which aim at incorporating new information to the already acquired knowledge without accessing previous data. Specifically, this paper focuses on those linear dimensionality reduction methods with orthogonal matrix constraints based on global loss function, due to the extensive use of their batch approaches versus other linear alter…
On semi-fredholm properties of a boundary value problem inR + n
1988
The paper considers a boundary value problem with the help of the smallest closed extensionL ∼ :H k →H k 0×B h 1×...×B h N of a linear operatorL :C (0) ∞ (R + n ) →L(R + n )×L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) ∞ (R + n )) denotes the linear space of smooth functionsR n →C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 ∞ , resp.),L(R n−1) is the Schwartz class of functionsR n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ∼) and for the uniqueness of solutionsL ∼ U=F are expressed. In addition, ana prio…
Description of the retention behaviour of solutes in micellar liquid chromatography with organic modifiers: Comparison of two methods
1995
Two methods for the description of the retention behaviour of solutes in micellar liquid chromatography are compared. One of them divides the parameter space into triangular subspaces, fitting a different equation in each subspace. The second method makes use of a unique equation, valid in the whole parameter space. In both cases, equations of the type log k=f (μ, ϕ), and 1/k=f (μ, ϕ), (μ and ϕ are the concentration of surfactant and alcohol, respectively), were used to describe the retention. The use of the hyperbolic function, 1/k=c0+c1μ+c3μϕ, to describe the whole parameter space yielded the best prediction. When a small portion of the parameter space was modelled, a simpler hyperbolic f…
A general framework for a class of non-linear approximations with applications to image restoration
2018
Este artículo se encuentra disponible en la página web de la revista en la siguiente URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042717301188 Este es el pre-print del siguiente artículo: Candela, V., Falcó, A. & Romero, PD. (2018). A general framework for a class of non-linear approximations with applications to image restoration. Journal of Computational and Applied Mathematics, vol. 330 (mar.), pp. 982-994, que se ha publicado de forma definitiva en https://doi.org/10.1016/j.cam.2017.03.008 This is the pre-peer reviewed version of the following article: Candela, V., Falcó, A. & Romero, PD. (2018). A general framework for a class of non-linear approximations with applic…