von Below, Joachim Can one hear the shape of a network? (English) Zbl 0973.35143 Ali Mehmeti, Felix (ed.) et al., Partial differential equations on multistructures. Proceedings of the conference, Luminy, France. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 219, 19-36 (2001). From the introduction: We show that, in contrast to the one-dimensional domain case, one cannot recover the shape of a network from the spectrum of its Laplacian under the continuity condition at ramification nodes and the Kirchhoff condition at all vertices. Thus, in that regard, networks behave like higher-dimensional objects. Moreover, we shall discuss the eigenvalue asymptotics as well as the distinction of network immanent eigenvalues from those stemming from single branches.For the entire collection see [Zbl 0960.00045]. Cited in 20 Documents MSC: 35P05 General topics in linear spectral theory for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35P20 Asymptotic distributions of eigenvalues in context of PDEs Keywords:ramification nodes; Kirchhoff condition; eigenvalue asymptotics PDFBibTeX XMLCite \textit{J. von Below}, Lect. Notes Pure Appl. Math. 219, 19--36 (2001; Zbl 0973.35143)