[Turkmath:4865] İ.Ü. Matematik Bölüm Semineri

[TEMHA ERKOÇ YILMAZTÜRK]

Merhabalar,

28.04.2021 tarihinde  saat 13.15 te Hacettepe Üniversitesinden  Dr. Öğr.
Üyesi  Nazife Erkurşun Özcan   başlık ve özeti aşağıda verilen bir konuşma
yapacaktır. Seminer Zoom programı üzerinden online yapılacaktır. Katılmak
isteyenlerin katılım bilgilerini alabilmeleri için "
huseyinuysal at istanbul.edu.tr "  adresine mail atmaları gerekmektedir.


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*Başlık:*  Ergodicities and perturbations of Markov C0- semigroups on
abstract states spaces

*Özet:* It is a well-known fact that the asymptotic behavior of certain
physical systems constitutes an integral part of physics and mathematics.
The solutions of equations are typically expressed by one-parameter
operator semigroups, and therefore, it is essential to know their long-term
behavior. One needs to have effective methods and techniques for the
examination of their asymptotic behavior. Great attention has been
attracted to the study of the connection between uniform ergodicities and
ergodic coefficients of semigroups defined on the classical function
spaces. However, in those investigations, the limiting operator was taken
as a rank-one projection. If one wants to consider the limiting operators
as some projections then the standard ergodic coefficient is no longer
effective. Consequently, a generalized Dobrushin ergodicity coefficient
δP(T)  for Markov operators (acting on an abstract state space) concerning
a projection P has been introduced.
The main goal of the talk is to explore stability and perturbation bounds
for positive C0-semigroups defined on abstract state spaces using a
generalized Dobrushin ergodicity coefficient. It is worth noting that we
also establish that the uniform and weak stabilities of time average Markov
operators through the generalized ergodicity coefficient shed new light on
this subject.

.
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İyi günler dileğiyle,

Temha

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