# Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures

@article{Pankrashkin2011UnitaryDR, title={Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures}, author={Konstantin Pankrashkin}, journal={Journal of Mathematical Analysis and Applications}, year={2011}, volume={396}, pages={640-655} }

## 26 Citations

### An example of unitary equivalence between self-adjoint extensions and their parameters

- Mathematics
- 2013

### Boundary Value Problems, Weyl Functions, and Differential Operators

- MathematicsMonographs in Mathematics
- 2020

The book under review is a comprehensive treatment of boundary value problems from the unifying point of view of boundary triplets, offering a panoramic view ranging from abstract problems to…

### Scattering on periodic metric graphs

- MathematicsReviews in Mathematical Physics
- 2020

We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and eigenvalues of the…

### Spectral Theory of Infinite Quantum Graphs

- MathematicsAnnales Henri Poincaré
- 2018

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths…

### Schrödinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra

- Mathematics
- 2021

### Spectral estimates for infinite quantum graphs

- MathematicsCalculus of Variations and Partial Differential Equations
- 2018

We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the…

### Zero Measure and Singular Continuous Spectra for Quantum Graphs

- Mathematics
- 2019

We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a non-trivial singular continuous…

### Zero Measure and Singular Continuous Spectra for Quantum Graphs

- MathematicsAnnales Henri Poincaré
- 2020

We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a non-trivial singular continuous…

### Eigenfunctions of Laplacians on periodic metric graphs

- Mathematics2016 Days on Diffraction (DD)
- 2016

We consider the Kirchhoff Laplacians on equilateral periodic metric graphs. We present results about spectral properties of these operators: 1) the decomposition of the metric Laplacians into a…

### Laplacians on infinite graphs: discrete vs continuous

- Mathematics
- 2021

There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a…

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