An Algebraic Approach to Implicit Evolution Equations

• Autorzy: Wha-Suck Lee , Niko Sauer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 58D25: Equations in function spaces; evolution equations
• 47D99: None of the above, but in this section
• 47D06: One-parameter semigroups and linear evolution equations
• 34K32: Implicit equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: 63
• Numer: 1
• Strony: 33-40

Daty

wydano

2015

Twórcy

autor

Wha-Suck Lee

• Department of Mathematics and Applied Mathematics, University of Pretoria, 0028 Pretoria, South Africa

autor

Niko Sauer

• Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa

Identyfikatory

DOI

10.4064/ba63-1-5