Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Dixmier trace

Toeplitz operator

Hankel operator

Bergman space

Hardy

space

strictly pseudoconvex domain

pseudodifferential operator

Levi

form

weighted bergman kernels

noncommutative residue

integral-operators

toeplitz

pseudodifferential operator

Publication and Content Type

ref (subject category)

art (subject category)