Essential spectra of tensor product Hilbert complexes and the \(\overline{\partial}\)-Neumann problem on product manifolds

DOI10.1016/j.jfa.2016.06.004zbMath1350.58009arXiv1508.01749OpenAlexW1913403630MaRDI QIDQ738781

Franz Berger

Publication date: 16 August 2016

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.01749

zbMATH Keywords

essential spectrumLaplacian\(\overline{\partial}\)-Neumann problemproduct manifoldselliptic complexesHilbert complexes

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Differential complexes (58J10) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

On some spectral properties of the weighted \(\overline\partial\)-Neumann operator ⋮ Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below

Cites Work

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• The Cauchy-Riemann equations on product domains
• Compactness of the \(\bar{\partial}\)-Neumann operator on singular complex spaces
• The stability of the Euler characteristic for Hilbert complexes
• Compactness of the solution operator to \(\overline\partial\) in weighted \(L^{2}\)-spaces
• The \({\overline{\partial}}\)-Neumann problem on product domains in \({\mathbb{C}^{n}}\)
• The Kuenneth formula for Hilbert complexes
• Hilbert complexes
• Complex geometry. An introduction
• The \(\bar \partial\) Neumann problem and Schrödinger operators
• Lectures on the \(L^2\)-Sobolev theory of the \(\bar\partial\)-Neumann problem
• Holomorphic Morse inequalities and Bergman kernels
• \(L^2\)-properties of the \(\overline{\partial}\) and the \(\overline{\partial}\)-Neumann operator on spaces with isolated singularities
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Applications of Pluripotential Theory to Algebraic Geometry
• Spectrum of the $\overline {\partial }$-Neumann Laplacian on polydiscs
• Positivity of the $\bar\partial$-Neumann Laplacian
• Compactness of the $\overline\partial$-Neumann Operator
• Spectrum of the complex Laplacian on product domains
• Shorter Notes: When Proper Maps are Closed
• Hilbert Space Methods in the Theory of Harmonic Integrals

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