Microlocal analysis for Gelfand--Shilov spaces and evolution equations
Välkommen till föreläsningen i seminarieserien i matematik.
We study Gelfand--Shilov ultradistribution spaces of Beurling type by means of the short-time Fourier transform (STFT). It is known that the growth and smoothness indices appear as exponential growth parameters of the STFT for ultradistributions, and as corresponding decay parameters for test functions. It is thus natural to define an anisotropic global wave front set which is anisotropically conic on phase space.
The talk is devoted to this wave front set. We state a condition on the wave front set of the Schwartz kernel of a linear operator which implies continuity and propagation of singularities. We apply the result to the study of propagation of singularities for a class of evolution equations that extends the Schr\"odinger equation for the free particle.
The talk is based on joint work with M. Cappiello and L. Rodino.