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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.
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 -