Super Toeplitz operators on line bundles

DOI10.1007/BF02930984zbMath1104.32001arXivmath/0406032OpenAlexW1992169229MaRDI QIDQ2434057

Robert J. Berman

Publication date: 31 October 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406032

zbMATH Keywords

asymptotic expansionToeplitz operatorBergman kernelline bundlessemi-positive curvature

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

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Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics ⋮ BERGMAN KERNELS AND EQUILIBRIUM MEASURES FOR POLARIZED PSEUDO-CONCAVE DOMAINS ⋮ Quantum ergodic sequences and equilibrium measures ⋮ Local Demailly-Bouche's holomorphic morse inequalities ⋮ Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles ⋮ Berezin transform in polynomial bergman spaces ⋮ Restricted Bergman kernel asymptotics

Cites Work

• Bergman kernels and local holomorphic Morse inequalities
• On a set of polarized Kähler metrics on algebraic manifolds
• A direct approach to Bergman kernel asymptotics for positive line bundles
• Spectral theory for tensor products of Hermitian holomorphic line bundles
• Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Sampling in weighted \(L^p\) spaces of entire functions in \(\mathbb{C}^n\) and estimates of the Bergman kernel
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