Convolutors of translation-modulation invariant Banach spaces of ultradistributions
arXiv:2106.01244 · doi:10.1016/j.jmaa.2021.125759
Abstract
We study the space of tempered ultradistributions whose convolutions with test functions are all contained in a given translation-modulation invariant Banach space of ultradistributions. Our main result will be the first structural theorem for the aforementioned space. As an application we consider several extensions of convolution.
37 pages
References in corpus (7)
- On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution
- On weighted inductive limits of spaces of ultradifferentiable functions and their duals
- Translation-modulation invariant Banach spaces of ultradistributions
- Topological properties of convolutor spaces via the short-time Fourier transform
- Optimal embeddings of ultradistributions into differential algebras
- On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth
- On the space of ultradistributions vanishing at infinity