Joe J. Perez
Unitary representations of unimodular Lie groups in Bergman spaces.
Tue, 09/14/2010 - 15:01 — SomNambulAuthors: Joe J. Perez, Giuseppe Della Sala
Subjects: Representation Theory
AbstractFor an arbitrary unimodular Lie group $G$, we construct strongly continuous
unitary representations in the Bergman space of a naturally constructed
strongly pseudoconvex neighborhood of $G$ in the complexification of its
underlying manifold.A transversal Fredholm property for the $\bar\partial$-Neumann problem on $G$-bundles.
Wed, 12/23/2009 - 16:01 — SomNambulAuthors: Joe J. Perez
Subjects: Complex Variables
AbstractLet $M$ be a strongly pseudoconvex complex $G$-manifold with compact quotient
$M/G$. We provide a simple condition on forms $\alpha$ sufficient for the
regular solvability of the equation $\square u=\alpha$ and other problems
related to the $\bar\partial$-Neumann problem on $M$.Subelliptic boundary value problems and The $G$-Fredholm Property.
Wed, 09/09/2009 - 22:08 — SomNambulAuthors: Joe J. Perez
Subjects: Complex Variables
AbstractLet $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and
$M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also
a complex manifold satisfying a local subelliptic estimate. In this work, we
show that if $G$ acts by holomorphic transformations in $M$, then the Laplacian
$\square=\bar\partial^{*}\bar\partial+\bar\partial\bar\partial^{*}$ on $M$ has
the following properties: The kernel of $\square$ restricted to the forms
$\Lambda^{p,q}$ with $q>0$ is a closed, $G$-invariant subspace in
$L^{2}(M,\Lambda^{p,q})$ of finite $G$-dimension.Subelliptic boundary value problems and The $G$-Fredholm Property.
Wed, 09/09/2009 - 22:08 — SomNambulAuthors: Joe J. Perez
Subjects: Complex Variables
AbstractLet $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and
$M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also
a complex manifold satisfying a local subelliptic estimate. In this work, we
show that if $G$ acts by holomorphic transformations in $M$, then the Laplacian
$\square=\bar\partial^{*}\bar\partial+\bar\partial\bar\partial^{*}$ on $M$ has
the following properties: The kernel of $\square$ restricted to the forms
$\Lambda^{p,q}$ with $q>0$ is a closed, $G$-invariant subspace in
$L^{2}(M,\Lambda^{p,q})$ of finite $G$-dimension.
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