scholarly journals Bergman kernels of elementary Reinhardt domains

2020 ◽  
Vol 306 (1) ◽  
pp. 67-93
Author(s):  
Debraj Chakrabarti ◽  
Austin Konkel ◽  
Meera Mainkar ◽  
Evan Miller
Keyword(s):  
Reinhardt Domains ◽  
Bergman Kernels

Generalized reinhardt domains

1991 ◽  
Vol 1 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Eric Bedford ◽  
Jiri Dadok
Keyword(s):  
Reinhardt Domains

scholarly journals BERGMAN KERNELS AND EQUILIBRIUM MEASURES FOR POLARIZED PSEUDO-CONCAVE DOMAINS

2010 ◽  
Vol 21 (01) ◽  
pp. 77-115 ◽  
Author(s):  
ROBERT J. BERMAN
Keyword(s):  
Toeplitz Operators ◽  
Equilibrium Measure ◽  
Markov Property ◽  
General Setting ◽  
Space Structure ◽  
Tensor Power ◽  
Bergman Kernels ◽  
Equilibrium Measures ◽  
Holomorphic Sections ◽  
Positive Line Bundle

Let X be a domain in a closed polarized complex manifold (Y,L), where L is a (semi-) positive line bundle over Y. Any given Hermitian metric on L induces by restriction to X a Hilbert space structure on the space of global holomorphic sections on Y with values in the k-th tensor power of L (also using a volume form ωn on X. In this paper the leading large k asymptotics for the corresponding Bergman kernels and metrics are obtained in the case when X is a pseudo-concave domain with smooth boundary (under a certain compatibility assumption). The asymptotics are expressed in terms of the curvature of L and the boundary of X. The convergence of the Bergman metrics is obtained in a more general setting where (X,ωn) is replaced by any measure satisfying a Bernstein–Markov property. As an application the (generalized) equilibrium measure of the polarized pseudo-concave domain X is computed explicitly. Applications to the zero and mass distribution of random holomorphic sections and the eigenvalue distribution of Toeplitz operators will be described elsewhere.

Mapping properties of the Bergman projections on elementary Reinhardt domains

2021 ◽  
Vol 71 (4) ◽  
pp. 831-844
Author(s):  
Shuo Zhang
Keyword(s):  
Sobolev Spaces ◽  
Bergman Projection ◽  
Reinhardt Domain ◽  
Reinhardt Domains ◽  
Multi Index ◽  
Bergman Projections

Abstract The elementary Reinhardt domain associated to multi-index k = (k 1, …, k n ) ∈ ℤ n is defined by ℋ ( k ) : = { z ∈ D n : z k   is defined and   | z k | < 1 } . $$\mathcal{H}(\mathbf{k}):=\{z\in\mathbb{D}^n: z^{\mathbf{k}}\ \text{is defined and}\ |z^{\mathbf{k}}|<1\}.$$ In this paper, we study the mapping properties of the associated Bergman projection on L p spaces and L p Sobolev spaces of order ≥ 1.

scholarly journals The spectrum of the Leray transform for convex Reinhardt domains in C2

2009 ◽  
Vol 257 (9) ◽  
pp. 2780-2819 ◽  
Author(s):  
David E. Barrett ◽  
Loredana Lanzani
Keyword(s):  
Reinhardt Domains

scholarly journals Reinhardt domains in CΛ

1977 ◽  
Vol 61 (3) ◽  
pp. 735-738
Author(s):  
Getulio Katz
Keyword(s):  
Reinhardt Domains

scholarly journals On bounded Reinhardt domains

1974 ◽  
Vol 50 (2) ◽  
pp. 119-123 ◽  
Author(s):  
Toshikazu Sunada
Keyword(s):  
Reinhardt Domains
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