Analytic holonomicity of real C$^{\mathrm{exp}}$-class distributions
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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.20167
- arXiv:
- arXiv:2403.20167
- Bibcode:
- 2024arXiv240320167A
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Logic;
- Mathematics - Representation Theory