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<p>In the paper Łysik (Ann Fenn Math 43:475–482, 2018) a characterization of real analytic functions in terms of integral means over Euclidean balls is given. The characterization enables us to define analytic functions on metric measure spaces. Here we introduce Dunkl analytic functions with respect to a Coxeter–Weyl group of reflections on Euclidean space and a nonnegative multiplicity function as those continuous functions for which a suitable mean value function is expressed by a convergent power series. In the main theorem we show that the Dunkl analytic functions are smooth.</p>

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Smoothness of the Dunkl analytic functions

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Grzegorz Łysik

摘要

In the paper Łysik (Ann Fenn Math 43:475–482, 2018) a characterization of real analytic functions in terms of integral means over Euclidean balls is given. The characterization enables us to define analytic functions on metric measure spaces. Here we introduce Dunkl analytic functions with respect to a Coxeter–Weyl group of reflections on Euclidean space and a nonnegative multiplicity function as those continuous functions for which a suitable mean value function is expressed by a convergent power series. In the main theorem we show that the Dunkl analytic functions are smooth.