Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions

Avraham Aizenbud; Raf Cluckers; Michel Raibaut; Tamara Servi

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arXiv · 2403.20167

Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions

Avraham Aizenbud·Raf Cluckers·Michel Raibaut·Tamara Servi

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Abstract

We introduce a notion of distributions on $\mathbb{R}^n$, called distributions of C$^{{\mathrm{exp}}}$-class, based on wavelet transforms of distributions and the theory from Cluckers, Comte, Miller, Rolin, Servi (2018) about C$^{{\mathrm{exp}}}$-class functions. We prove that the framework of C$^{{\mathrm{exp}}}$-class distributions is closed under natural operations, like push-forward, pull-back, derivation and anti-derivation, and, in the tempered case, Fourier transforms. Our main result is the (real analytic) holonomicity of all distributions of C$^{{\mathrm{exp}}}$-class.

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BibTeX RIS

Avraham Aizenbud, Raf Cluckers, Michel Raibaut, Tamara Servi. 2024-03-29. Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions. https://arxiv.org/abs/2403.20167

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