New point view of spectral gap in functional spaces for birth-death processes

Abstract

Constructing some proper functional spaces, we obtain the corresponding norm for the operator (−ℒ)−1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5(3): 379–515], for transient birth-death processes.