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An Algebraic Approach to Implicit Evolution Equations
Wha-Suck Lee 1   ; Niko Sauer 2
1 Department of Mathematics and Applied Mathematics University of Pretoria 0028 Pretoria, South Africa
2 Department of Mathematics and Applied Mathematics University of Pretoria, South Africa
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 33-40 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba63-1-5
Keywords: banach algebra homomorphism convolution algebra integrable functions essence kisy skis equivalent formulation hille yosida theorem analytic semigroups study implicit evolution equations notion empathy happens appropriate semigroup approach based intertwining families evolution operators families pseudo resolvents paper kisy ski approach adapted empathy theory adaptation highlights essential differences between semigroup theory theory empathy

Wha-Suck Lee  1   ; Niko Sauer  2

1 Department of Mathematics and Applied Mathematics University of Pretoria 0028 Pretoria, South Africa
2 Department of Mathematics and Applied Mathematics University of Pretoria, South Africa 
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Wha-Suck Lee; Niko Sauer. An Algebraic Approach to Implicit Evolution Equations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 33-40. doi: 10.4064/ba63-1-5

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