Submission date: 29 March 2024

Abstract:

We introduce a notion of distributions on ℝ^n, called distributions of C^{exp}-class, based on wavelet transforms of distributions and the theory from [6] about C^{exp}-class functions. We prove that the framework of C^{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^{exp}-class.

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Full text arXiv 2403.20167: pdf, ps.