Trace formulae for Schrödinger systems on graphs

Authors: CHUAN-FU YANG, ZHEN-YOU HUANG, XIAO-PING YANG

Abstract: For Schrödinger systems on metric graphs with \delta'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.

Keywords: Schrödinger systems, metric graph, \delta'-type conditions, trace formula, Ambarzumyan-type theorem.

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