https ://core .ac .uk /download /pdf /70984529 .pdf Reply to this discussion with your thoughts on this paper . Here are some guidelines and suggestions : Your reply should aim to help you and other students gain deeper understanding of the points in the pdf. Can you summarize the construction of the Laplace transform? Why do we require s to be positive? . Does every function have a Laplace transform ? Can you provide a counterexample There's also a relationship between power series and the Laplace transform . Can you explain it? . If you are familiar with inner products of functions , is there anything to be said about the Laplace transform and the standard inner product of function spaces