12 research outputs found
Symmetric diffusions with polynomial eigenvectors
25 pagesInternational audienceWe describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension, some basic examples arise from compact Lie groups. We give a complete description of the bounded sets on which such operators may live. We then provide a classification of those sets when the polynomials are ordered according to their usual degree
Almost exponential maps and integrability results for a class of horizontally regular vector fields
We show a higher order integrability theorem for distributions generated by a
family of vector fields under a horizontal regularity assumption on their
coefficients. We use as chart a class of almost exponential maps which we
discuss in detailsComment: arXiv admin note: material from arXiv:1106.2410v1, now three separate
articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520
Operator theory and function theory in Drury-Arveson space and its quotients
The Drury-Arveson space , also known as symmetric Fock space or the
-shift space, is a Hilbert function space that has a natural -tuple of
operators acting on it, which gives it the structure of a Hilbert module. This
survey aims to introduce the Drury-Arveson space, to give a panoramic view of
the main operator theoretic and function theoretic aspects of this space, and
to describe the universal role that it plays in multivariable operator theory
and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page
On Hardy and BMO Spaces for Grushin Operator
We study Hardy and BMO spaces associated with the Grushin operator. We first prove atomic and maximal functions characterizations of the Hardy space. Further we establish a version of Fefferman–Stein decomposition of BMO functions associated with the Grushin operator and then obtain a Riesz transforms characterization of the Hardy space