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About 3,426 papers for “Continuous linear operator”

Linear continuous system discretization using a new general delta operator

Carmen Torres, V. Gimenez, F. M. de Monasterio · 2004

To find the discrete mathematical model that is going to represent, by the best way, a real continuous system, is one of the problems that any control engineer will probably need to solve, since any real control system includes digital components. Up to now, the problem of finding that discrete model, was generally solved by means of the Z-transform and the shift operator but, at high sampling speed and due to numerical sensitivity problems, these methods have, in general, become not valid. For this reason, some alternatives to these discretization methods have been developed. In this paper we present on of these methods, which is based on the General Delta operator and transform. This new method offers not only a model but a set of models where each one of them depends on the value given to a certain parameter called n/sub 2/. In this article we have developed an analytical study about the optimal selection of this parameter using the sampling period for adapting the adequate parameter. We will also present an illustrative example in order to show the effect that a change in the sampling period has over the system output.

Cited by 1

New Types of Continuous Linear Operator in Probabilistic Normed Space

Iqbal H. Jebril · 2014

Abstract. In this paper, new types of continuous linear operator, such as continuous, strongly continuous, weakly continuous and sequentially continu-ous linear operators, in probabilistic normed space are introduced. Also, the relation between the boundedness and continuity of these linear operators in probabilistic normed spaces is studied. 2000 Mathematics Subject Classification: 54E70 Key words and phrases: Probabilistic normed space, continuous linear oper-ators. 1. Introduction and

Cited by 0

Characterizing weak-operator continuous linear functionals on $B(H)$ constructively

Douglas Bridges · Documenta Mathematica · 2011

Let B(H) be the space of bounded operators on a not-necessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T\leadsto \langle Tx,y\rangle . We also prove that the identification of weak- and strong-operator continuous linear functionals on B(H) cannot be established constructively.

Cited by 1Open access

Integral Representations for Continuous Linear Functionals in Operator-Initiated Topologies

Walter Roth · 2000

Abstract. On a given cone (resp. vector space) Q we consider an initial topology and order induced by a family of linear operators into a second cone P which carries a locally convex topology. We prove that monotone linear functionals on Q which are continuous with respect to this initial topology may be represented as certain integrals of continuous linear functionals on P. Based on the Riesz representation theorem from measure theory, we derive an integral version of the Jordan decomposition for linear functionals on ordered vector spaces.

Cited by 0

Some properties of continuous linear operator in topological vector PN spaces

Gaemi, M.B., Lafuerza Guillén, Bernardo, Saiedinezhad, S. · Repositorio de Patentes de la Universidad de Almería (Universidad de Almería) · 2014

The notion of a probabilistic metric space corresponds to the situations when we do not know exactly the distance. Probabilistic Metric space was introduced by Karl Menger. Alsina , Schweizer and Sklar gave a general definition of a probabilistic normed space based on the definition of Menger. In this note we study the PN spaces which are topological vector spaces and the open mapping and closed graph Theorems in this spaces are proved.

Cited by 0Open access

Characterization Conditions for a Kind of Norm Continuous Linear Operator Family

Liang Xie · 2007

Let A and B be the generator of C1-regularized semigroups {S(t)t≥0,andC2-regularized semigroups {T(t)}t≥0, Seperately.denote by △(t) for S(t)-T(t),we got some sufficient conditions in terms of the resolvents of A and B for norm continutity of the operator family △(t) in Hilbert space.

Cited by 0

A Linear Discontinuous Galerkin Approximation for the Continuous Slowing Down Operator

Maximo S. Lazo, Jim E. Morel · Nuclear Science and Engineering · 1986

A linear discontinuous Galerkin treatment is developed for the continuous slowing down operator. Multigroup Legendre coefficients are derived that allow this treatment to be implemented in standard Sn codes, A synthetic acceleration scheme is developed to accelerate the outer iterations required by this treatment. A computational comparison between the diamond difference treatment and the linear discontinuous treatment is given.

Cited by 23Open access

Existence of Nonzero, Linear and Continuous Operator between Two Musielak-Orlicz Spaces

Ewa Kasior, Marek Wisła · Taiwanese Journal of Mathematics · 2011

Let $X, Y$ be linear topological subspaces of the space of all measurable functions over a $\sigma$-finite, atomless and complete measure space $\Omega$. The question of existence of a nonzero, linear continuous operator $T: X \to Y$ is a natural extension of the question "does X admit a nonzero, linear continuous functional?". In case of $X = L^\Phi(\Omega)$, $Y = L^\Psi(\Omega)$ being Orlicz spaces Ph.Turpin ([11]) gave a criterion telling when there is no nonzero, linear and continuous operator between $L^\Phi(\Omega)$ and $L^\Psi(\Omega)$. That result was extended to the case of Musielak-Orlicz spaces by A.K.Kalindé, R.Płuciennik and M.Wisła ([2, 8]) but only necessary conditions have been presented by them - in fact conditions assuring that there is no nonzero, linear and continuous operator between $L^\Phi(\Omega)$ and $L^\Psi(\Omega)$. In this paper we give inverse theorems to the Kalindé and Płuciennik-Wisła theorems. Generally speaking we state that there exists a nonzero, linear and continuous operator if and only if it there exists a set $A \subset \Omega$ of positive and finite measure such that the inclusion operator $i: L^\Phi(A) \to L^\Psi(A)$ is nonzero and continuous.

Cited by 0Open access

Results of Hankel Semigroup of Linear Operator as Eventually Uniform Continuous Semigroup

Akinola Yussuff Akinyele, Jude Babatunde Omosowon, Moses Adebowale Aasa et al. · General Mathematics · 2022

Abstract This paper consists of Hankel results of ω -order reversing partial contraction as a semigroup of linear operator. Spectral mapping theorem was investigated and it was established that ω -order reversing partial contraction mapping is an eventually uniform continuous semigroup in which we showed that the proof of the extension of T ( t ) to a C 0 -semigroup ̂ T ( t ) on a space ̂ X containing X isometrically bounded. The space is constructed in such a way that the spectrum of the generator A of T ( t ) coincides with the spectrum of the generator  of ̂ T ( t ) and the approximate point spectrum of A coincides with the point spectrum of  .

Cited by 0Open access

TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES

Klatenia Selawati, Ch. Rini Indrati · Journal of Fundamental Mathematics and Applications (JFMA) · 2023

In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operators on asymmetric normed spaces is focused on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.

Cited by 0Open access

Documenta Math. 597 Characterising Weak-Operator Continuous Linear Functionals on B(H) constructively

Douglas S. Bridges, Communicated Anil Nerode · 2011

Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H. Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T � 〈Tx,y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be established constructively.

Cited by 0

Block pulse operator method for parameter identification problems in non-linear continuous systems

Wang Shienyu · International Journal of Systems Science · 1991

An approximation algorithm for use in parameter identification problems governed by non-linear differential equations is developed by means of a block pulse operator (BPO). Three different schemes of the identification algorithms can be constructed. The basic idea of the method based on BPO is to convert the problems of parameter identification in the original function space into equivalent approximating identification problems in the image space of BPO. In the image space, the algorithm for solving the approximating problems may be considerably simplified. We have proved that the solutions of the approximating problems converge to the solution of the original parameter identification problem. Sufficient conditions are given for the convergence. Two examples are presented to illustrate the utility of the method.

Cited by 1