24,817 research outputs found
Some remarks on the Krein--von Neumann extension of different Laplacians
We discuss the Krein--von Neumann extensions of three Laplacian-type
operators -- on discrete graphs, quantum graphs, and domains. In passing we
present a class of one-dimensional elliptic operators such that for any infinitely many elements of the class have -dimensional null
space.Comment: 13 page
On the Spectrum of Holonomy Algebras
Connections on a trivial bundle MxG can be identified with their holonomy
maps, i.e. with homomorphisms of a groupoid of paths in M into the gauge group
G.
For a connected compact G, various algebras depending on the set of the
smooth connections through their holonomy maps have been introduced in the
literature, called cylindrical and holonomy algebras. We discuss the relations
between these algebras and the consistence of their spectra.Comment: 23 pages, no figures, to appear in J.Geom.Phy
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