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Radial Schur multipliers on some generalisations of trees

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Abstract

We give a characterisation of radial Schur multipliers on finite products of trees. The equivalent condition is that a certain generalised Hankel matrix involving the discrete derivatives of the radial function is a trace class operator. This extends Haagerup, Steenstrup and Szwarc's result for trees. The same condition can be expressed in terms of Besov spaces on the torus. We also prove a similar result for products of hyperbolic graphs and provide a sufficient condition for a function to define a radial Schur multiplier on a finite dimensional CAT(0) cube complex.

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ensl-01894550 , version 1 (12-10-2018)

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Ignacio Vergara. Radial Schur multipliers on some generalisations of trees. 2018. ⟨ensl-01894550⟩
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