ANNALES POLONICI MATHEMATICI LXXIV (2000) Laplace integrals in partial differential equations in papers of Bogdan Ziemian by Grzegorz  Lysik (Warszawa) Abstract. Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals. 1. Problem. Let P be a polynomial in n complex variables and consider the tempered distribution  E 0 = reg 1 P (0 + i·) , which is the regularization of the function R n ∋ β → 1/P (0 + iβ) to a tem- pered distribution on R n . The problem consists essentially in establishing a real Laplace inversion formula for  E 0 . Recall that it is easy to obtain an imaginary inversion formula for  E 0 : namely one takes the inverse Fourier transform of  E 0 , (1) E 0 (y) = reg iR n e −yθ P (θ) dθ. Then E 0 is a tempered fundamental solution of the operator P (D y ), i.e. P (D y )E 0 = cδ (0) . It follows from the classical results of Ehrenpreis [Eh] and Palamodov [P] that E 0 can be represented by (2) E 0 (y)= Char P e −yθ µ(dθ) where µ is a bounded Radon measure on the complex characteristic set of P , Char P = {z ∈ C n : P (z)=0}. 2000 Mathematics Subject Classification : 35A20, 35C15. Key words and phrases : linear partial differential equations, Laplace representations, Leray residue formula, Nilsson integrals. The paper contains also some ideas presented by Bogdan Ziemian on his seminar. [43]