A remark on the Laplace transform (Q2203450)

In this article, the authors considered the problem of the inverse Laplace transform of the entire function \(\cos(\sqrt{z})\) associated to the Cauchy problem for the solution of the heat equation in a cyclindrical domain. The authors calculated the inverse Laplace transform of \(\cos(\sqrt{z})\) in particular and the Laplace transform of analytical functionals in general. A result regarding Carleman formula and the existence of a solution of the problem is given.