比利时vs摩洛哥足彩
,
university of california san diego
****************************
analysis colloquium
louis boutet de monvel
university of paris
logarithmic trace of the szego and toeplitz projectors
abstract:
in my book with v. guillemin ``the spectral theory of toeplitz operators'', we defined toeplitz projectors on a compact contact manifold, which are analogues of the szego projector on a strictly pseudo-convex boundary. if $x$ is a contact manifold, the kernel of a toeplitz projector, just as the szego kernel, has a holonomic singularity including a polar and a logarithmic term, and its trace is well defined. \vskip .1in \noindent we show that the trace of a toeplitz operator only depends on the contact structure of $x$. if $x$ is the three sphere equipped with any contact form, this invariant vanishes (y. eliashberg has shown there are many nonisomorphic such contact forms); this makes it not unlikely that the trace vanishes identically.
host: salah baouendi
april 26, 2005
10:30 am
ap&m 6438
****************************