Autor:	Kamber, Amitay
Zdroj:	Israel Journal of Mathematics; Oct2019, Vol. 234 Issue 2, p863-905, 43p
Abstrakt:	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 a (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+^ε for every ε > 0. We generalize the result to operators on edges and to bipartite graphs. The work is based on a combinatorial interpretation of representationtheoretic ideas. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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