Pedro José Miana (Universidad de Zaragoza) impartirá la conferencia "Koopman semigroups in functions and sequences Lebesgue spaces"

Pedro José Miana (Universidad de Zaragoza) impartirá la conferencia 

"Koopman semigroups in functions and sequences Lebesgue spaces"

Abstract:

Composition operators in dynamic systems are often referred to as Koopman operators, in honor of the French-American mathematician Bernard Osgood Koopman (1900–1981). In this talk, we present a brief introduction to Koopman semigroups. Next, we present three examples of weighted Koopman semigroups defined on fractional Lebesgue-Sobolev spaces on the half real line.
We are also interested in connecting Koopman semigroups in Lebesgue spaces of functions 𝐿􀯣 (ℝ􀬾) and semigroups in Lebesgue spaces of sequences lpfor 1 ≤ 𝑝 < ∞. To do this, we use a certain Poisson transformation 𝒫: 𝐿p (ℝ+) → lp and its adjoint 𝒫∗, which allows us to transfer the properties of the semigroup from one space to another. Two Koopman semigroups in l􀯣 are presented and related to the canonical Koopman semigroup in 𝐿p(ℝ+).
In the last part of the talk, we introduce operators that extend Cesáro operators (called Chen-type integral operators) subordinate to these Koopman semigroups in 𝐿p(ℝ+) and lp.
The first results of this article are a joint work with Verónica Poblete, from the University of Chile, and are published in Monatshefte für Mathematik, 206, (2025). The second part of the talk contains results from a preprint available on the Arxiv platform.

Hora: 18:00h

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