Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators

DOI10.1016/j.jfa.2009.06.011zbMath1179.47041arXiv0807.0095OpenAlexW2168936024MaRDI QIDQ841494

Daniel Alpay, Jussi Behrndt

Publication date: 17 September 2009

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

Full work available at URL: https://arxiv.org/abs/0807.0095

zbMATH Keywords

Nevanlinna functiontrace formulaelliptic operatorWeyl functionDirichlet-to-Neumann map\(Q\)-functionKrein's formula

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Elliptic equations and elliptic systems (35J99)

Related Items (22)

Titchmarsh-Weyl theory for Schrödinger operators on unbounded domains ⋮ Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh \(M\)-functions, and a generalized index of unbounded meromorphic operator-valued functions ⋮ An Inverse Problem of Calderón Type with Partial Data ⋮ On non-homogeneous Robin reflection for harmonic functions ⋮ Elliptic boundary value problems with \(\lambda \)-dependent boundary conditions ⋮ Discrete symplectic systems, boundary triplets, and self-adjoint extensions ⋮ Isospectral measures ⋮ Spectral asymptotics for resolvent differences of elliptic operators with \(\delta\) and \(\delta^{'}\)-interactions on hypersurfaces ⋮ Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems ⋮ Heat flow for Dirichlet-to-Neumann operator with critical growth ⋮ Restrictions and extensions of semibounded operators ⋮ Finite-dimensional Self-adjoint Extensions of a Symmetric Operator with Finite Defect and their Compressions ⋮ The Dirichlet-to-Neumann operator on exterior domains ⋮ Dirichlet-to-Neumann maps on bounded Lipschitz domains ⋮ The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials ⋮ Donoghue-type \(m\)-functions for Schrödinger operators with operator-valued potentials ⋮ Spectral theory of elliptic operators in exterior domains ⋮ A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains ⋮ The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates ⋮ A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains ⋮ A note on an operator-theoretic approach to classic boundary value problems for harmonic and analytic functions in complex plane domains ⋮ Perturbation of essential spectra of exterior elliptic problems

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