instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Groups on Fréchet spaces and the heat equation solution for negative time
Seminario PHD
We present a general method for generation of uniformly continuous groups on abstract Fréchet spaces and we apply it to a such space of distributions, namely $FL^2_{loc}$, so that if a(D) is a pseudodifferential operator with constant coefficients defined on it then its Cauchy problem has a unique solution. We conclude that the solution of the heat equation on $FL^2_{loc}$ for all time extends the standard solution on Hilbert spaces for positive time.