Harmonic Analysis on Graphs: Maximal Bounds for Cartesian Powers of Finite Graphs

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چکیده

My research in graph theory focuses on asymptotic maximal bounds for Cartesian powers of finite graphs. This line of inquiry was opened up by [4], in which the authors proved that the maximal spherical averaging operator on the N -dimensional hypercube K 2 satisfies a bound in the L 2 norm independent of the dimension N . That is, if Sk(x) := {y : d(x, y) = k} in the graph distance metric on K 2 , the L 2 norm of the function

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تاریخ انتشار 2015