Displaying similar documents to “Approximation theorem for evolution operators”

A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

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A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.

Compact operators and approximation spaces

Fernando Cobos, Oscar Domínguez, Antón Martínez (2014)

Colloquium Mathematicae

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We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.

The norm convergence of a Magnus expansion method

András Bátkai, Eszter Sikolya (2012)

Open Mathematics

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We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.

Disjoint hypercyclic operators

Luis Bernal-González (2007)

Studia Mathematica

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We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.

On a class of Szász-Mirakyan type operators

Zbigniew Walczak (2008)

Czechoslovak Mathematical Journal

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The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.

On the norm of a projection onto the space of compact operators

Joosep Lippus, Eve Oja (2007)

Studia Mathematica

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Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than...

Approximation by Durrmeyer-type operators

Vijay Gupta, G. S. Srivastava (1996)

Annales Polonici Mathematici

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We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.

On integral type generalizations of positive linear operators

O. Duman, M. A. Özarslan, O. Doğru (2006)

Studia Mathematica

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We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute the rates of statistical convergence. Furthermore, we deal with the local approximation and the rth order generalization of our operators.

Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1

Xiao-Ming Zeng, Vijay Gupta (2009)

Open Mathematics

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The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators M ^ n , α ( f , x ) for α ≥ 1 have been studied in [Comput. Math. Appl., 39 (2000), 1-13]. The aim of this paper is to deal with the pointwise approximation of the operators M ^ n , α ( f , x ) for the other case 0 < α < 1. By means of some new techniques and new inequalities we establish an estimate formula on the rate of convergence of the operators M ^ n , α ( f , x ) for the case 0 < α < 1. In the end we propose the q-analogue of...

Approximation of abstract linear integrodifferential equations

Hirokazu Oka, Naoki Tanaka (2000)

Studia Mathematica

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This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.