The Trace Formula for Quantum Graphs with General Self Adjoint Boundary Conditions
نویسندگان
چکیده
منابع مشابه
The trace formula for quantum graphs with general self adjoint boundary conditions
We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums over periodic orbits on the graph. This includes trace formulae with, respectively, absolutely and conditionally convergent periodic orbit sums; the convergenc...
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Let A : D(A) ⊆ H → H be an injective self-adjoint operator and let τ : D(A) → X, X a Banach space, be a surjective linear map such that ‖τφ‖X ≤ c ‖Aφ‖H. Supposing that Range (τ ) ∩ H = {0}, we define a family AτΘ of self-adjoint operators which are extensions of the symmetric operator A|{τ=0} . Any φ in the operator domain D(A τ Θ) is characterized by a sort of boundary conditions on its univoc...
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ژورنال
عنوان ژورنال: Annales Henri Poincaré
سال: 2009
ISSN: 1424-0637,1424-0661
DOI: 10.1007/s00023-009-0399-7