2012/12/12 by Ralf Rueckriemen, Rueckriemen, Ralf
Mathematics · #34E05 #35J10 #35P15 #47A75 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34E05 #msc:35J10 #msc:35P15 #msc:47A75
paper · pdf · doi:10.48550/arxiv.1212.2840
arxiv created 2012/12/12 · arxiv updated 2012/12/13
We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that depend on the potential in a universal way. These coefficients are spectral invariants, we compute the first few of them.