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Asymptotic expansion of polyanalytic Bergman kernels | | Haakan Hedenmalm
; Antti Haimi
; | | Date: |
4 Mar 2013 | | Abstract: | We consider mainly the Hilbert space of bianalytic functions on a given
domain in the plane, square integrable with respect to a weight. We show how to
obtain the asymptotic expansion of the corresponding bianalytic Bergman kernel
for power weights, under the standard condition on those weights. This is
well-known in the analytic setting, from the work of e.g. Tian, Yay’u,
Zelditch, Catlin, et al. We remark that a bianalytic function may be identified
with a vector-valued analytic function, supplied with a locally singular metric
on the vectors. | | Source: | arXiv, 1303.0720 | | Services: | Forum | Review | PDF | Favorites | |
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