Displaying similar documents to “On the Sharpness of Non-Optimal Approximation for Semigroup Operators.”

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.

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.

Decomposing and twisting bisectorial operators

Wolfgang Arendt, Alessandro Zamboni (2010)

Studia Mathematica

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Bisectorial operators play an important role since exactly these operators lead to a well-posed equation u'(t) = Au(t) on the entire line. The simplest example of a bisectorial operator A is obtained by taking the direct sum of an invertible generator of a bounded holomorphic semigroup and the negative of such an operator. Our main result shows that each bisectorial operator A is of this form, if we allow a more general notion of direct sum defined by an unbounded closed projection....

Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II

Piotr Budzyński, Jan Stochel (2009)

Studia Mathematica

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In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-space by positive definiteness of the Radon-Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of C₀-groups of composition operators on L²-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition...

Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces

Piotr Budzyński, Jan Stochel (2007)

Studia Mathematica

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Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group...

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.