Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains
Artikel i vetenskaplig tidskrift, 2010
Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of 2(n) Hankel operators on Bergman spaces of strictly pseudoconvex domains in C-n. The answer turns out to involve the dual Levi form evaluated on boundary derivatives of the symbols. Our main tool is the theory of generalized Toeplitz operators due to Boutet de Monvel and Guillemin.
pseudodifferential operator
form
strictly pseudoconvex domain
toeplitz
Toeplitz operator
Dixmier trace
space
noncommutative residue
Hardy
integral-operators
weighted bergman kernels
Hankel operator
Bergman space
Levi