Radial Schur multipliers on some generalisations of trees

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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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01894550
Contributor : Ignacio Vergara <>
Submitted on : Friday, October 12, 2018 - 3:24:29 PM
Last modification on : Saturday, October 13, 2018 - 1:09:13 AM

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  • HAL Id : ensl-01894550, version 1
  • ARXIV : 1803.06692

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

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