Pseudodifferential Operators on Periodic Graphs |
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Authors: | Vladimir?S?Rabinovich Email author" target="_blank">Steffen?RochEmail author |
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Institution: | 1.Instituto Politécnico Nacional,ESIME-Zacatenco,Mexico D.F.,Mexico;2.Technische Universit?t Darmstadt,Darmstadt,Germany |
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Abstract: | The main aim of the paper is Fredholm properties of a class of bounded linear operators acting on weighted Lebesgue spaces
on an infinite metric graph Γ which is periodic with respect to the action of the group
\mathbb Zn{{\mathbb {Z}}^n} . The operators under consideration are distinguished by their local behavior: they act as (Fourier) pseudodifferential operators
in the class OPS
0 on every open edge of the graph, and they can be represented as a matrix Mellin pseudodifferential operator on a neighborhood
of every vertex of Γ. We apply these results to study the Fredholm property of a class of singular integral operators and
of certain locally compact operators on graphs. |
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Keywords: | |
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