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PRODID:-//talks.bham.ac.uk//v3//EN
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CATEGORIES:Analysis Seminar
SUMMARY:Spectral multipliers and wave equation for sub-Lap
lacians - Sebastiano Nicolussi Golo (University of
Birmingham)
DTSTART:20181114T093000Z
DTEND:20181114T103000Z
UID:TALK3439AT
URL:/talk/index/3439
DESCRIPTION:Mihlin-Hörmander theorem gives the sharp Sobolev o
rder n/2 for a spectral multiplier of the Laplacia
n to define a bounded operator on L^p for all p∈(1
\,∞).\n\nWe study the same type of statements for
sub-Laplacians\, which are sub-elliptic operators
defined on sub-Riemannian manifolds. It is known t
hat the homogeneous dimension Q can play the same
role as n on certain sub-Riemannian manifolds. How
ever\, there are examples\, such as the Heisenberg
groups\, where Q>n but n/2 is again the sharp Sob
olev order. Here\, n is the topological dimension.
These results led to conjecture that the sharp So
bolev order for a Mihlin-Hörmander theorem is half
the topological dimension in a large class of sub
-Riemannian manifolds\, e.g.\, Carnot groups.\n\nW
e have proven that in no sub-Riemannian manifold t
he sharp Sobolev order can be lower than half the
topological dimension. For the proof\, we construc
t a partial Fourier integral representation of the
sub-Riemannian wave propagator. \n\nThis is a joi
nt work with Alessio Martini and Detlef Müller.
LOCATION:Poynting Small Lecture Theatre (S06)
CONTACT:Diogo Oliveira E Silva
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