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We show that the deficiency indices of the minimal Gaffney Laplacian on an infinite locally finite metric graph are equal to the number of finite volume graph ends. Moreover, we provide criteria, formulated in terms of finite volume graph ends, for the Gaffney Laplacian to be closed.
We study the symmetry properties of the spectra of normalized Laplacians on signed graphs. We find a new machinery that generates symmetric spectra for signed graphs, which includes bipartiteness of unsigned graphs as a special case. Moreover, we pro
We prove a variant of the Davies-Gaffney-Grigoryan Lemma for the continuous time heat kernel on graphs. We use it together with the Li-Yau inequality to obtain strong heat kernel estimates for graphs satisfying the exponential curvature dimension inequality.
In this note, we prove the sharp Davies-Gaffney-Grigoryan lemma for minimal heat kernels on graphs.
We consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path Laplacian ope
We study the multiplicative Hilbert matrix, i.e. the infinite matrix with entries $(sqrt{mn}log(mn))^{-1}$ for $m,ngeq2$. This matrix was recently introduced within the context of the theory of Dirichlet series, and it was shown that the multiplicati