Dynamical Systems Seminar: Dr. Harrison Gaebler | Department of Mathematics

Dynamical Systems Seminar: Dr. Harrison Gaebler

Event Information
Event Location: 
GAB 461
Event Date: 
Friday, September 30, 2022 - 2:00pm

Title: Growth of orbits for operator semigroups on Banach spaces with Schauder bases

Abstract: Let $X$ be a Banach space with a normalized (Schauder) basis $(b_k)_k$ and let $\{T(t)\}_{t\geq 0\}$ be a $C_{0}$-semigroup on $X$ with generator $A:D(A)\subset X\to X$. I will in this talk introduce a new estimate for the semigroup orbits of initial data in $D(A^{2})$ that have with respect to $(b_{k})_{k}$ ``absolutely summable graph norm." This result is noteworthy because (1) there is no requirement that $z\mapsto R(z,A)x$ has a bounded analytic extension to the right half-plane and (2) the only structural condition on $X$ is the existence of $(b_{k})_{k}$.

Thinking about UNT?

It's easy to apply online. Join us and discover why we're the choice of over 42,000 students.

Apply now