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In this paper we study the optimal stopping problem for L\'evy processesstudied by Novikov and Shiryayev, Stochastics, 2007 In particular, we areinterested in finding the representing measure of the value function. It isseen that that this can be expressed in terms of the Appell polynomials. Animportant tool in our approach and computations is the Wiener-Hopffactorization.

Optimal stopping, Appell polynomials and Wiener-Hopf factorization representations of excessive functions of L\'evy processes