# Our updated research pages

We would like to share our update on the research pages: Functional inequalities and Nonharmonic analysis.

Functional inequalities: Here we present a historical overview of original Hardy inequality.

G. H. Hardy reported Harald Bohr as saying ’all analysts spend half their time hunting through the literature for inequalities which they want to use but cannot prove’.

Nonharmonic analysis: We show the difference between harmonic vs nonharmonic analysis and give a survey of our recent works.

Harmonic analysis: symmetries in the underlying space, e.g. working with $e^{2\pi i x\cdot\xi}$ on $\mathbb T^n$ with $\xi\in\mathbb Z^n$; more generally, working with representations of compact, nilpotent, or more general locally compact type I groups;

Nonharmonic analysis: no symmetries in the underlying space, e.g. working with $e^{2\pi i x\cdot\xi}$ on $\mathbb T^n$ with $\xi\not\in\mathbb Z^n$; This name was given by Paley and Wiener.