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

Published 29 Mar 2024 in math.AG, math.LO, and math.RT | (2403.20167v1)

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 [6] 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 antiderivation, and, in the tempered case, Fourier transforms. Our main result is the (real analytic) holonomicity of all distributions of C$^{{{\mathrm{exp}}}$-class.}