A note on Fourier coefficients of Poincar\'e series

We give a short and "soft" proof of the asymptotic orthogonality of Fourier coefficients of Poincar\'e series for classical modular forms as well as for Siegel cusp forms, in a qualitative form.Comment: 10 page

A note on Poincar\'e- and Friedrichs-type inequalities

We introduce a simple criterion to check coercivity of bilinear forms on subspaces of Hilbert-spaces. The presented criterion allows to derive many standard and non-standard variants of Poincar\'e- and Friedrichs-type inequalities with very little effort

A note on some Poincar\'e inequalities on convex sets by Optimal Transport methods

We show that a class of Poincar\'e-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly unbounded.Comment: 13 page