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Home » Hamiltonian Postdoc Workshop: The effect of threshold energy obstructions on the L 1 → L∞ dispersive esti- mates for some Schr ̈odinger type equations

Seminar

Hamiltonian Postdoc Workshop: The effect of threshold energy obstructions on the L 1 → L∞ dispersive esti- mates for some Schr ̈odinger type equations November 19, 2018 (11:15 AM PST - 12:00 PM PST)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Ebru Toprak (University of Illinois at Urbana-Champaign)
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In this talk, I will discuss the differential equation iut = Hu, H := H0 + V ,

where V is a decaying potential and H0 is a Laplacian related operator. In particular,

I will focus on when H0 is Laplacian, Bilaplacian and Dirac operators. I will discuss

how the threshold energy obstructions, eigenvalues and resonances, effect the L

1 → L∞

behavior of e

itHPac(H). The threshold obstructions are known as the distributional so-

lutions of Hψ = 0 in certain dimension dependent spaces. Due to its unwanted effects

on the dispersive estimates, its absence have been assumed in many work. I will mention

our previous results on Dirac operator and recent results on Bilaplacian operator under

different assumptions on threshold energy obstructions.

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