Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions
Algebraic Geometry
2026-01-21 v2 Logic
Representation Theory
Abstract
We introduce a notion of distributions on , called distributions of C-class, based on wavelet transforms of distributions and the theory from Cluckers, Comte, Miller, Rolin, Servi (2018) about C-class functions. We prove that the framework of C-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-class.
Cite
@article{arxiv.2403.20167,
title = {Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions},
author = {Avraham Aizenbud and Raf Cluckers and Michel Raibaut and Tamara Servi},
journal= {arXiv preprint arXiv:2403.20167},
year = {2026}
}
Comments
Proposition 3.13 gets a new, corrected proof in the new section 4 on algebraic holonomicity. To appear in Trans. Amer. Math. Soc