An Algebraic Approach to Implicit Evolution Equations
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 33-40
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Wha-Suck Lee 1 ; Niko Sauer 2
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author = {Wha-Suck Lee and Niko Sauer},
title = {An {Algebraic} {Approach} to {Implicit} {Evolution} {Equations}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {33--40},
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volume = {63},
number = {1},
year = {2015},
doi = {10.4064/ba63-1-5},
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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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