In this thesis we are interested in Uncertainty Principles. Published by Heisenberg in 1927, the uncertainty principle was a key discovery in the early development of quantum theory. It implies that it is impossible to simultaneously measure the present position and momentum of a particle. The aim of this thesis is to extend some results about annihilating pairs in two contexts. In the first part we extend the local uncertainty principle, the Benedicks-Amrein-Berthier uncertainty principle, the Shubin-Vakilian-Wolff uncertainty principle and the Logvinenko-Sereda uncertainty principle for the Fourier-Bessel transform. This uncertainty principles state that a function and its Fourier- Bessel transform cannot be simultaneously well concentrated. The aim of the second part is to deal with uncertainty principles in finite the dimensional settings witch is linked to the theory of compresseve sensing. Our result extends previously known qualitative uncertainty principles into more quantitative for the discrete Fourier transform/ short time Fourier transform.
