2022/02/11 by Rodino, Luigi, Wahlberg, Patrik
#35A18 #35A27 #35S05 #46F05 #46F12 #47G30 #58J47 #81S30 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2202.05543
We introduce an anisotropic global wave front set of Gelfand--Shilov ultradistributions with different indices for regularity and decay at infinity. The concept is defined by the lack of super-exponential decay along power type curves in the phase space of the short-time Fourier transform. This wave front set captures the phase space behaviour of oscillations of power monomial type, a k a chirp signals. A microlocal result is proved with respect to pseudodifferential operators with symbol classes that give rise to continuous operators on Gelfand--Shilov spaces. We determine the wave front set of certain series of derivatives of the Dirac delta, and exponential functions.