Wilson bases and ultradistributions
Nenad Teofanov
TL;DR
This paper characterizes Gelfand-Shilov spaces and their duals of ultradistributions using Wilson bases with exponential decay, extending existing results to the Roumieu case with two different proofs.
Contribution
It introduces a new characterization of ultradistribution spaces via Wilson bases and extends prior results to the Roumieu setting.
Findings
Characterization of Gelfand-Shilov spaces using Wilson bases
Extension of results to the Roumieu case
Two different proofs provided for the main results
Abstract
We give a characterization of Gelfand-Shilov type spaces of test functions and their dual spaces of tempered ultradistributions by the means of Wilson bases of exponential decay. We offer two different proofs, and extend known results to the Roumieu case.
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