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Empathy theory and the Laplace transform

Niko Sauer (1997)

Banach Center Publications

This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.

Endomorphisms of the Cuntz algebras

Roberto Conti, Jeong Hee Hong, Wojciech Szymański (2011)

Banach Center Publications

This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor set. An identification...

Endpoint bounds for convolution operators with singular measures

E. Ferreyra, T. Godoy, M. Urciuolo (1998)

Colloquium Mathematicae

Let S n + 1 be the graph of the function ϕ : [ - 1 , 1 ] n defined by ϕ ( x 1 , , x n ) = j = 1 n | x j | β j , with 1< β 1 β n , and let μ the measure on n + 1 induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with μ is L p - L q bounded.

Enlargements of operators between locally convex spaces.

José A. Conejero (2007)

RACSAM

In this note we study three operators which are canonically associated with a given linear and continuous operator between locally convex spaces. These operators are defined using the spaces of bounded sequences and null sequences. We investigate the relation between them and the original operator concerning properties, like being surjective or a homomorphism.

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