## Proceedings of Symposia in Pure Mathematics (802)

### BibTeX

@MISC{802proceedingsof,

author = {},

title = {Proceedings of Symposia in Pure Mathematics},

year = {802}

}

### OpenURL

### Abstract

Thin tubes in mathematical physics, global analysis and spectral geometry

### Citations

300 |
Pseudodifferential Operators and Spectral Theory
- Shubin
- 1987
(Show Context)
Citation Context ...ents, II: Pseudodifferential operators. The classical pseudodifferential operator (ΨDO) calculus provides a systematic way to study the resolvent of an elliptic operator on a compact manifold X (see (=-=Shubin, 1987-=-) for example). More precisely, if R(λ, p, p ′ ) is the integral kernel of the resolvent, where p, p ′ ∈ X and λ is the spectral parameter, then the standard ΨDO parametrix construction gives an expli... |

57 | Analysis on manifolds with corners - Melrose |

53 | Free electron network model for conjugated systems - Ruedenberg, Scherr - 1953 |

28 | Eta invariants and manifolds with boundary - Müller - 1994 |

27 | Branched quantum wave guides with Dirichlet boundary conditions: the decoupling case
- Post
(Show Context)
Citation Context ...s around a graph, with Neumann boundary conditions, see 3.4.3 (but with a worse error O( √ ε) in (3.26); we loosely follow (Exner and Post, 2007) which we refer to for more details, and to (Exner and =-=Post, 2005-=-) for the full proof along these lines). We need to find operators J : L 2 (Ω0) → L 2 (Ωε) and J ′ : L 2 (Ωε) → L 2 (Ω0) respecting the domains of ∆ which yield good comparison estimates of norms and ... |

24 | Quantum bound states in a classically unbounded system of crossed wires, Phys. Rev. B39 - Schult, Ravenhall, et al. - 1989 |

22 | Scattering solutions in networks of thin fibers: small diameter asymptotics - Molchanov, Vainberg |

18 | Spectral convergence of quasi-one-dimensional spaces - Post |

11 | Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten. 1. Berlin: Akademie-Verlag - Mazja, Nazarov, et al. - 1991 |

10 | Transition from a network of thin fibers to the quantum graph: an explicitly solvable model - Molchanov, Vainberg |

8 | A star-graph model via operator extension - Pavlov - 2007 |

7 | Adiabatic decomposition of the ζ-determinant and Dirichlet to Neumann operator - Park, Wojciechowski - 2005 |

6 | Laplace operator in networks of thin fibers: spectrum near the threshold, arXiv:0704.2795v1 [math-ph - Molchanov, Vainberg - 2007 |

6 | Adiabatic decomposition of the ζ-determinant and scattering theory - Park, Wojciechowski |

4 | Analytische Störung der isolierten Punkteigenwerte eines beschränkten - unknown authors - 1936 |

2 | Decomposition of the ζ-determinant for the Laplacian on manifolds with cylindrical end - Loya, Park |

2 | Pseudodifferential operators, corners and singular limits - Geom - 1992 |

2 | Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants - Müller, Müller |