A note on an operator-theoretic approach to classic boundary value problems for harmonic and analytic functions in complex plane domains

DOI10.1007/s00020-010-1779-6zbMath1203.30041arXiv0908.4449OpenAlexW2592660791MaRDI QIDQ5962006

Vladimir Ryzhov

Publication date: 16 September 2010

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.4449

zbMATH Keywords

Riemann-Hilbert problemPoincaré problem\(M\)-operatorsspectral boundary value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General theory of partial differential operators (47F05) Boundary value problems in the complex plane (30E25)

Related Items (3)

Linear boundary-value problems described by Drazin invertible operators ⋮ Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems ⋮ On the spectral boundary value problems and boundary approximate controllability of linear systems

Cites Work

• \(M\) operators: A generalisation of Weyl--Titchmarsh theory
• The abstract Titchmarsh-Weyl \(M\)-function for adjoint operator pairs and its relation to the spectrum
• On the spectral theory of elliptic differential operators. I
• Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators
• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• Boundary value problems for elliptic partial differential operators on bounded domains
• Multi-dimensional versions of a determinant formula due to Jost and Pais
• Weyl-Titchmarsh function of an abstract boundary value problem, operator colligations, and linear systems with boundary control
• Variations on a theme of Jost and Pais
• Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains
• Spectral inclusion and spectral exactness for PDEs on exterior domains
• The Krein–von Neumann extension and its connection to an abstract buckling problem
• Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains
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