A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains
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Publication:542035
DOI10.1007/s11854-011-0002-2zbMath1231.47044arXiv0907.1750OpenAlexW1999382308MaRDI QIDQ542035
Marius Mitrea, Friedrich Gesztesy
Publication date: 8 June 2011
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0907.1750
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05)
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Cites Work
- On the nature of the Laplace-Beltrami operator on Lipschitz manifolds
- \(M\) operators: A generalisation of Weyl--Titchmarsh theory
- Eigenvalue problems on exterior domains and Dirichlet to Neumann maps
- Weyl function and spectral properties of self-adjoint extensions
- The abstract Titchmarsh-Weyl \(M\)-function for adjoint operator pairs and its relation to the spectrum
- Perturbation of spectra and Krein extensions
- Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators
- Spectral theory for perturbed Krein Laplacians in nonsmooth domains
- Nonselfadjoint operators, infinite determinants, and some applications
- Boundary value problems for elliptic partial differential operators on bounded domains
- The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients
- On symmetries in the theory of finite rank singular perturbations
- Weyl-Titchmarsh function of an abstract boundary value problem, operator colligations, and linear systems with boundary control
- Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities
- Triplet extensions. I: Semibounded operators in the scale of Hilbert spaces
- Non-self-adjoint accretive extensions of positive operators and theorems of Friedrichs-Krein-Phillips
- Friedrichs and Krein extensions of positive operators and holomorphic contraction semigroups
- Generalized resolvents and the boundary value problems for Hermitian operators with gaps
- Self-adjoint operators
- \(Q\)-functions and SC-resolvents of nondensely defined Hermitian contractions
- The classical moment problem as a self-adjoint finite difference operator
- An addendum to Krein's formula
- Dirichlet forms and symmetric Markov processes
- The von Neumann problem for nonnegative symmetric operators
- Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren. I
- Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
- On Krein's formula in indefinite metric spaces
- The inhomogeneous Dirichlet problem in Lipschitz domains
- Geometric measure theory.
- The extension theory of Hermitian operators and the moment problem
- Boundary value problems and Hardy spaces associated to the Helmholtz equation in Lipschitz domains
- A continuum of unusual self-adjoint linear partial differential operators
- Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains
- Variations on a theme of Jost and Pais
- Resolvents of self-adjoint extensions with mixed boundary conditions
- On the Krein and Friedrichs extensions of a positive Jacobi operator
- Positive selfadjoint extensions of positive symmetric operators
- Inverse spectral theory for symmetric operators with several gaps: scalar-type Weyl functions
- Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
- On a formula of the generalized resolvents of a nondensely defined Hermitian operator
- An unusual self-adjoint linear partial differential operator
- Steklov Eigenproblems and the Representation of Solutions of Elliptic Boundary Value Problems
- Boundary relations and their Weyl families
- On the point spectrum of ℋ︁–2‐singular perturbations
- Spectral Characterization of the Trace Spaces ${H^s({\partial \Omega})}$
- Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
- A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials
- SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
- Scattering matrices and Weyl functions
- M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
- Self-adjoint extensions of restrictions
- Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition
- Krein resolvent formulas for elliptic boundary problems in nonsmooth domains
- Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains
- The theory of extensions and explicitly-soluble models
- On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
- THE THEORY OF BI-EXTENSIONS OF OPERATORS ON RIGGED HILBERT SPACES. UNBOUNDED OPERATOR COLLIGATIONS AND CHARACTERISTIC FUNCTIONS
- Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien
- On von Neumann’s problem in extension theory of nonnegative operators
- Spectral inclusion and spectral exactness for PDEs on exterior domains
- Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains
- On Matrix-Valued Herglotz Functions
- On Kreĭn's extension theory of nonnegative operators
- Sobolev and Besov Space Estimates for Solutions to Second Order PDE on Lipschitz Domains in Manifolds with Dini or Hölder Continuous Metric Tensors
- Geometry and stability of bubbles with gravity
- Abstract Boundary Conditions for Maximal Sectorial Extensions of Sectorial Operators
- The Krein–von Neumann extension and its connection to an abstract buckling problem
- Intermediate Hamiltonian via Glazman's splitting and analytic perturbation for meromorphic matrix‐functions
- Known and unknown results on elliptic boundary problems
- Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators
- Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains
- EXTENSIONS AND GENERALIZED RESOLVENTS OF A SYMMETRIC OPERATOR WHICH IS NOT DENSELY DEFINED
- Complex symplectic spaces and boundary value problems
- A remark on the Dirichlet-Neumann decoupling and the integrated density of states
- A Krein-like formula for singular perturbations of self-adjoint operators and applications
- On Krein's formula in the case of non-densely defined symmetric operators
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