Heisenberg uncertainty inequalities for locally compact abelian groups

Hartmut Führ

Heisenberg uncertainty inequalities for locally compact abelian groups

Functional Analysis 2026-06-29 v1

Authors: Hartmut Führ

Abstract

We prove a version of Heisenberg's uncertainty principle for a rather general class of locally compact abelian groups. We compare the lower bound provided by our approach with the optimal lower bound in the Euclidean case, and formulate the Heisenberg uncertainty principle for local fields.

Keywords

Heisenberg uncertainty principle locally compact abelian groups Fourier analysis local fields

Cite

@article{arxiv.2606.30079,
  title  = {Heisenberg uncertainty inequalities for locally compact abelian groups},
  author = {Hartmut Führ},
  journal= {arXiv preprint arXiv:2606.30079},
  year   = {2026}
}