Ultradifferentiable functions via the Laguerre operator

期刊论文
发表日期：

2025年7月6日

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Smiljana Jakšić,
Stevan Pilipović,
Nenad Teofanov,
Đorđe Vučković

摘要

We define and characterize ultradifferentiable functions and their corresponding ultradistributions on $\mathbb R^d_+$ $R_{+}^{d}$ using iterates of the Laguerre operator. The characterization is based on the decay or growth conditions of the coefficients in their Laguerre series expansion. We apply our results to establish an isomorphism between subspaces of Pilipović spaces on $\mathbb R^d$ $R^{d}$ , and the spaces of ultradifferentiable functions on $\mathbb R^d_+$ $R_{+}^{d}$ .