Hermitian symplectic geometry and the factorization of the scattering matrix on graphs

DOI10.1088/0305-4470/33/49/302zbMath0964.05042arXivmath-ph/0703031OpenAlexW2085371768MaRDI QIDQ2707812

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Publication date: 4 April 2001

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0703031

zbMATH Keywords

eigenvaluesspectrumcharacterizationscattering matrixeigenfunctionsymmetric operatorsLagrange planeHermitian symplectic spaces

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Special classes of linear operators (47B99)

Related Items (13)

On equi-transmitting matrices ⋮ The very unusual properties of the resolvent, heat kernel, and zeta function for the operator −d2∕dr2−1∕(4r2) ⋮ Continuity of the integrated density of states on random length metric graphs ⋮ On vertex conditions for elastic systems ⋮ On reflectionless equi-transmitting matrices ⋮ Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples ⋮ A general approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds ⋮ Inverse problems for Aharonov–Bohm rings ⋮ Exotic expansions and pathological properties of \(\zeta\)-functions on conic manifolds ⋮ Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone ⋮ Asymptotically isospectral quantum graphs and generalised trigonometric polynomials ⋮ Quantum fields on star graphs with bound states at the vertex ⋮ Spectral functions for the Schrödinger operator on R+ with a singular potential

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