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<p>In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these operators are sub-Laplacians in horizontal divergence form perturbed with a potential and their generalisations.</p>

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Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月24日

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  • Véronique Fischer,
  • Søren Mikkelsen

摘要

In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these operators are sub-Laplacians in horizontal divergence form perturbed with a potential and their generalisations.