We consider the fractional Klein--Gordon equation on $\mathbb{R}^d$ with space-dependent damping. Our main aim is to establish the equivalence between energy decay estimates of the equation and a kind of the uncertainty principle in Fourier analysis. In addition, we give a new sufficient condition for the polynomial decay using the equivalence. This is a joint work with Kotaro Inami (Nagoya University).

Note: This seminar will be held as a Zoom online seminar (only NLPDE seminar members may attend in person).