Subexponential decay (SD) is introduced as a weakening of rapid decay; permanence of SD/RD under amalgamated free products is proved with sharp distortion bounds, with applications to selflessness of reduced C*-algebras.
Holt, and Sarah Rees,Rapid decay is preserved by graph products, 2011
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Some remarks on decay in countable groups and amalgamated free products
Subexponential decay (SD) is introduced as a weakening of rapid decay; permanence of SD/RD under amalgamated free products is proved with sharp distortion bounds, with applications to selflessness of reduced C*-algebras.