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<p>We introduce the Riesz operator in the context of Gromov hyperbolic groups in order to investigate a one parameter family of non unitary and non tempered boundary Hilbertian representations of hyperbolic groups deforming the trivial representation to the standard boundary representation. We prove that asymptotic Schur’s relations occur for the representations we build. Moreover, up to normalization, the Riesz operator plays the role in the context of hyperbolic groups of the Knapp–Stein intertwiner for complementary series of Lie groups.</p>

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Riesz operators and some spherical representations for hyperbolic groups

  • 期刊论文

  • 发表日期：

    2025年2月3日

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  • Adrien Boyer,
  • Jean-Claude Picaud

摘要

We introduce the Riesz operator in the context of Gromov hyperbolic groups in order to investigate a one parameter family of non unitary and non tempered boundary Hilbertian representations of hyperbolic groups deforming the trivial representation to the standard boundary representation. We prove that asymptotic Schur’s relations occur for the representations we build. Moreover, up to normalization, the Riesz operator plays the role in the context of hyperbolic groups of the Knapp–Stein intertwiner for complementary series of Lie groups.