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Radial Schur multipliers on some generalisations of trees

Volume 249 / 2019

Ignacio Vergara Studia Mathematica 249 (2019), 59-109 MSC: Primary 46L07; Secondary 05C63, 47B10, 47B35, 30H25. DOI: 10.4064/sm180424-23-7 Published online: 22 February 2019

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.

Authors

  • Ignacio VergaraUMPA UMR 5669 CNRS
    ENS Lyon
    Université de Lyon
    69364 Lyon Cedex 07, France
    e-mail

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