Special issue of the 14th International Workshop on H-mode Physics and Transport Barriers (Fukuoka, Japan, 2013)

[摘要] We prove an analogue for trees of Sturmʼs oscillation theorem on the interlacing property of zeros of eigenfunctions of a Schrödinger operator. Let Γ bea finite tree, and  a combinatorial Schrödinger operator on Γ. If the eigenvectors of  are ordered according to increasing eigenvalues, and the verticescorresponding to zero coordinates are of degree at most two, then the zeros ofthe linear extensions of eigenvectors have the interlacing property.

[关键词] Schrödinger operator;tree;interlacing property;discrete nodaltheorem