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HANKEL OPERATORS AND THE DIXMIER TRACE ON STRICTLY PSEUDOCONVEX DOMAINS
"... Abstract. Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of 2n Hankel operators on Bergman spaces of strictly pseudoconvex domains in Cn. The answer turns out to involve the dual Levi form evaluated on boundary derivatives of the symbol ..."
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Abstract. Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of 2n Hankel operators on Bergman spaces of strictly pseudoconvex domains in Cn. 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. 1.
ANALYTIC CONTINUATION OF WEIGHTED BERGMAN KERNELS
"... Abstract. We show that the Bergman kernel Kα(x, y) on a smoothly bounded strictly pseudoconvex domain with respect to the weight ρ α, where −ρ is a defining function and α> −1, extends meromorphically in α to the entire complex plane. This is somewhat reminiscent of scattering poles or resonances ..."
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Abstract. We show that the Bergman kernel Kα(x, y) on a smoothly bounded strictly pseudoconvex domain with respect to the weight ρ α, where −ρ is a defining function and α> −1, extends meromorphically in α to the entire complex plane. This is somewhat reminiscent of scattering poles or resonances in scattering theory. With a small change, the assertion remains valid also for functions ρ of slightly more general type. 1.
Classification of Traces and Associated Determinants on OddClass Operators in Odd Dimensions
"... Abstract. To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of oddclass pseudodifferential operators of nonpositive order acting on smooth functions on a closed odddimensional manifold. By mean ..."
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Abstract. To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of oddclass pseudodifferential operators of nonpositive order acting on smooth functions on a closed odddimensional manifold. By means of the one to one correspondence between continuous traces on Lie algebras and determinants on the associated regular Lie groups, we give a classification of determinants on the group associated to the algebra of oddclass pseudodifferential operators with fixed nonpositive order. At the end we discuss two possible ways to extend the definition of a determinant outside a neighborhood of the identity on the Lie group associated to the algebra of oddclass pseudodifferential operators of order zero.
Documenta Math. 601 Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains
, 2009
"... Abstract. Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of 2n 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 symbo ..."
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Abstract. Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of 2n 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.
Classification of Traces and Associated Determinants on OddClass Operators in Odd Dimensions
"... Abstract. To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of oddclass pseudodifferential operators of nonpositive order acting on smooth functions on a closed odddimensional manifold. By mea ..."
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Abstract. To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of oddclass pseudodifferential operators of nonpositive order acting on smooth functions on a closed odddimensional manifold. By means of the one to one correspondence between continuous traces on Lie algebras and determinants on the associated regular Lie groups, we give a classification of determinants on the group associated to the algebra of oddclass pseudodifferential operators with fixed nonpositive order. At the end we discuss two possible ways to extend the definition of a determinant outside a neighborhood of the identity on the Lie group associated to the algebra of oddclass pseudodifferential operators of order zero.