445 research outputs found
On approximation of functions from Sobolev spaces on metric graphs
Some results on the approximation of functions from the Sobolev spaces on
metric graphs by step functions are obtained. The estimates are uniform with
respect to all graphs of a given finite length, and the constant factors in the
inequalities are sharp.Comment: 19 pages, 0 figure
Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
In the model suggested by Smilansky one studies an operator describing the
interaction between a quantum graph and a system of one-dimensional
oscillators attached at several different points in the graph. The present
paper is the first one in which the case is investigated. For the sake of
simplicity we consider K=2, but our argument is of a general character. In this
first of two papers on the problem, we describe the absolutely continuous
spectrum. Our approach is based upon scattering theory
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