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SUMMARY:Dario Prandi (CentraleSupelec)
DTSTART:20210108T150000Z
DTEND:20210108T160000Z
DTSTAMP:20260423T035720Z
UID:SRS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SRS/8/">Poin
 t interactions for 3D sub-Laplacians</a>\nby Dario Prandi (CentraleSupelec
 ) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThe aim of this semina
 r is to present some recent results on the essential self-adjointness of p
 ointed sub-Laplacians in three dimensions. These are the natural (non-nega
 tive) hypoelliptic operators $H$ associated with a sub-Riemannian structur
 e on a 3D manifold $M$\, with domain $\\operatorname{Dom}(H)=C^\\infty_c(M
 \\setminus \\{p\\})$\, for $p\\in M$.\n\nIf $M=\\mathbb{R}^n$ and the geom
 etry is Euclidean\, $H$ is the standard Laplacian. It is then well-known t
 hat $H$ is essentially self-adjoint with $\\operatorname{Dom}(H) =C^\\inft
 y_c(\\mathbb{R}^n\\setminus\\{p\\})$ if and only if $n\\ge 4$. This follow
 s\, for instance\, by the Euclidean Hardy inequality.\n\nIn this seminar w
 e show that\, unlike the Euclidean case\, pointed sub-Laplacians (as-socia
 ted with smooth measures) are essentially self-adjoint already for contact
  sub-Riemannian manifolds of\n(topological) dimension $3$. Although this i
 s not surprising\, since the Hausdorff dimension of these structures is $4
 $\, we will sow that this result cannot be deduced via Hardy inequalities 
 as in the Euclidean case but requires a much finer machinery. Indeed\, our
  strategy of proof is based on a localicazion argument which allows to red
 uce to the study of the 3D Heisenberg pointed sub-Laplacian. The essential
  self-adjoitness of the latter is then obtained by exploiting non-commutat
 ive Fourier transform techniques.\n\nThis is a joint work with R. Adami (P
 olitecnico di Torino\, Italy)\,  U. Boscain (CNRS &UPMC\, Sorbonne Univers
 ité\, France)\, and V. Franceschi (Università di Padova\, Italy).\n
LOCATION:https://researchseminars.org/talk/SRS/8/
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