An Algebraic Approach to Implicit Evolution Equations

Volume 63 / 2015

Wha-Suck Lee, Niko Sauer Bulletin Polish Acad. Sci. Math. 63 (2015), 33-40 MSC: 34K32, 47D06, 47D99, 58D25. DOI: 10.4064/ba63-1-5


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.


  • Wha-Suck LeeDepartment of Mathematics and Applied Mathematics
    University of Pretoria
    0028 Pretoria, South Africa
  • Niko SauerDepartment of Mathematics and Applied Mathematics
    University of Pretoria, South Africa

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