演講訊息 TALKS

摘要: In this seminar, we will first show the uniqueness theorem of Laplace transforms. To prove this, it suffices to prove Widder's inversion formula since the uniqueness is readily a consequence of Widder's inversion formula. This seminar also contains the convergence theorem of Laplace transforms which parallels the convergence theorem of Fourier transforms. Besides, we will prove Bernstein's Theorem and Feller's Tauberian Theorem, the first one says that a function is the Laplace transform of a measure if and only if it is completely monotone, the second one is about the asymptotic behavior of the distribution function as t goes to infinity. The motivation for choosing this topic is because it has an application in potential theory.