Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^p$ Expander Graphs   We discuss how graph expansion is related to the behavior of
$L^{p}$-functions on the covering tree. We show that the non-trivial
eigenvalues of the adjacency operator on aa $(q+1)$-regular graph are bounded
by $q^{1/p}+q^{(p-1)/p}$ - the $L^{p}$-norm of the operator on the covering
tree - if and only if properly averaged lifts of functions from the graph to
the tree lie in $L^{p+\epsilon}$ for every $\epsilon>0$. We generalize the
result to operators on edges and to bipartite graphs.
  The work is based on a combinatorial interpretation of
representation-theoretic ideas.

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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th