Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
11 - On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
Published online by Cambridge University Press: 14 August 2020
Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
Summary
In this expository paper weanswertwo fundamental questions concerning discrete magnetic Schrödinger operator associated with weighted graphs. We discuss when formal expressions of such operators give rise to self-adjoint operators, i.e., when they have self-adjoint realizations. If such self-adjoint realizations exist, we explore when they are unique.
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- Analysis and Geometry on Graphs and Manifolds , pp. 250 - 327Publisher: Cambridge University PressPrint publication year: 2020
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