منابع مشابه
Isospectral Graphs and Isospectral Surfaces
In memory of Hubert Pesce In this paper, we investigate the following question: to what extent is there a converse to the Theorem of Sunada Su] in the context of graphs? Our experience in dealing with the question, \Can one hear the shape of a drum?" is that the many facets of this question turn out to be surprisingly delicate. The present instance is no exception. We will rst present a partial...
متن کاملInformation Geometry of Positive Matrices and Isospectral Flow
A di erential-geometric structure of the manifold PD(n) of all the n n positive-de nite matrices is studied by means of informatin geometry. It is given by a pair of dual at a ne connections with an invariant Riemannian metric and a divergence function. Special attention is paid to the geometry induced in the isospectral submanifolds and the natural gradient ow induced in it. Its relation to th...
متن کاملIsospectral compression and other useful isospectral transformations of dynamical networks.
It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). We demonstrated that it is possible to reduce a network, considered as a graph, to a smaller network with fewer vertices and edges while preserving the spectrum (or spectral information) of the original network [L. A. Bunimovich ...
متن کاملCompactness of isospectral sets
© Séminaire de Théorie spectrale et géométrie (Grenoble), 1991, tous droits réservés. L’accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi...
متن کاملOn Isospectral Arithmetical Spaces
We study the relationship between the arithmetic and the spectrum of the Laplacian for manifolds arising from congruent arithmetic subgroups of SL(1, D), where D is an indefinite quaternion division algebra defined over a number field F . We give new examples of isospectral but non-isometric compact, arithmetically defined varieties, generalizing the class of examples constructed by Vigneras. T...
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ژورنال
عنوان ژورنال: Nonlinear Differential Equations and Applications NoDEA
سال: 2014
ISSN: 1021-9722,1420-9004
DOI: 10.1007/s00030-014-0276-z