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Empathy theory and the Laplace transform

100%

Sauer N.

Banach Center Publications

1997

tom 38

nr 1

325-338

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.

An Algebraic Approach to Implicit Evolution Equations

63%

Lee W.-S., Sauer N.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

tom 63

nr 1

33-40

A Banach algebra homomorphism on the convolution algebra of integrable functions is the essence of Kisyński's equivalent formulation of the Hille-Yosida theorem for analytic semigroups. For the study of implicit evolution equations the notion of empathy happens to be more appropriate than that of semigroup. This approach is based upon the intertwining of two families of evolution operators and two families of pseudo-resolvents. In this paper we show that the Kisyński approach can be adapted to empathy theory. The adaptation highlights the essential differences between semigroup theory and the theory of empathy.

Ograniczanie wyników

1 Banach Center Publications

1 Bulletin of the Polish Academy of Sciences. Mathematics

2 Sauer N.

1 Lee W.-S.

1 2015

1 1997

Wyniki wyszukiwania

Empathy theory and the Laplace transform

An Algebraic Approach to Implicit Evolution Equations