An Algebraic Approach to Implicit Evolution Equations

Wha-Suck Lee, and Niko Sauer. "An Algebraic Approach to Implicit Evolution Equations." Bulletin of the Polish Academy of Sciences. Mathematics 63.1 (2015): 33-40. <http://eudml.org/doc/281338>.

@article{Wha2015,
abstract = {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.},
author = {Wha-Suck Lee, Niko Sauer},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {evolution operators; implicit evolution equation; Hille-Yosida-Kisyński generation},
language = {eng},
number = {1},
pages = {33-40},
title = {An Algebraic Approach to Implicit Evolution Equations},
url = {http://eudml.org/doc/281338},
volume = {63},
year = {2015},
}

TY - JOUR
AU - Wha-Suck Lee
AU - Niko Sauer
TI - An Algebraic Approach to Implicit Evolution Equations
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 1
SP - 33
EP - 40
AB - 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.
LA - eng
KW - evolution operators; implicit evolution equation; Hille-Yosida-Kisyński generation
UR - http://eudml.org/doc/281338
ER -