Dixmier trace and the Fock space

We give criteria for products of Toeplitz and Hankel operators on the Fock (Segal-Bargmann) space to belong to the Dixmier class, and compute their Dixmier trace. At the same time, analogous results for the Weyl pseudodifferential operators are also obtained.Comment: 23 pages, no figure

Big Hankel Operators on Vector-Valued Fock Spaces in Cd\mathbb {C}^dCd

International audienceWe study big Hankel operators acting on vector-valued Fock spaces with radial weights in C-d. We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators

Bergman-type projections in generalized Fock spaces

24 pages, no figuresInternational audienceWe give criteria for boundedness of the associated Bergman-type projections on Lp-spaces on Cn with respect to generalized Gaussian weights exp(-|z|^2m). Complete characterization is obtained for