Work

Analytic holonomicity of real C^{_rj}-class distributions

Year: 2026

Type: article

Abstract: We introduce a notion of distributions on R n \mathbb {R}^{n} , called distributions of C e x p \mathscr {C}^{\mathrm {exp}} -class, based on wavelet transforms of distributions and the theory of Cluckers, Comte, Miller, Rolin, and Servi [Duke Math. J. 167 (2018), pp. 1239–1309] about C e x p \mathscr {C}^{\mathrm {exp}} -class functions. We prove that the framework of C e x p \mathscr {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 e x p \mathscr {C}^{\mathrm {exp}} -class.

Source: Transactions of the American Mathematical Society Series B

DOI: 10.1090/btran/250

Authors: Avraham Aizenbud, Raf Cluckers, Michel Raibaut, Tamara Servi

Language: English

Topic: Mathematical and Theoretical Analysis

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,750

Funders: Israel Science Foundation, KU Leuven

Awards: G1765914219, G2764565460, G5761572133, G8080811220