On the Laplace transform for tempered holomorphic functions

In order to discuss the Fourier-Sato transform of not necessarily conic sheaves, we compensate the lack of homogeneity by adding an extra variable. We can then obtain Paley-Wiener type results, using a theorem by Kashiwara and Schapira on the Laplace transform for tempered holomorphic functions. As a key tool in our approach, we introduce the subanalytic sheaf of holomorphic functions with exponential growth, which should be of independent interest.