By Guerzhoy P.
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J. Phys. A, 19(18):L1173–L1177, 1986.  F. Chung, A. -T. Yau. Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Comm. Anal. , 8(5):969– 1026, 2000. K. Chung. Spectral graph theory, volume 92 of CBMS Regional Conference Series in Mathematics. Conference Board of the Mathematical Sciences, Washington, DC, 1997.  Y. Colin de Verdi`ere. Spectres de graphes, volume 4 of Cours Sp´ ecialis´es. Soci´et´e Math´ematique de France, Paris, 1998.  T. Coulhon and L.
A function y satisfying the diﬀerential equations may now be expressed as y = (C(λ, ·), S(λ, ·))ξ for an appropriate ξ ∈ C2r . In particular, the function y = (C(λ, ·), S(λ, ·))ξ satisﬁes the interface conditions (and hence is a solution of Ly = λy) precisely if ξ is in the kernel of the (2r − n0 ) × 2r-matrix J(λ) = I(C(λ, ·), S(λ, ·)). 4. Initial value problems Initial value problems do, in general, not have unique solutions on trees. This causes the main diﬀerences in the treatment of inverse problems on trees when compared to intervals.