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Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains

M. Englis ; Genkai Zhang (Institutionen för matematiska vetenskaper, matematik)
Documenta Mathematica (1431-0643). Vol. 15 (2010), p. 601-622.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: 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

Denna post skapades 2010-10-14. Senast ändrad 2015-12-17.
CPL Pubid: 127612


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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