Images of function and distribution spaces under the Bargmann transform

By J. Toft. 2014

83 citations recorded by the source corpus.

We consider a broad family of test function spaces and their dual (distribution) spaces. The family includes Gelfand–Shilov spaces, and a family of test function spaces introduced by Pilipović. We deduce different characterizations of such spaces, especially under the Bargmann transform and the Short-time Fourier transform. The family also include a test function space, whose dual space is mapped by the Bargmann transform bijectively to the set of entire functions.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7736d3e0ff89c5e6d98905544f5fddda8cab1604