Professor Francesco Mainardi
University of Bologna, Bologna, Italy
Complete monotonicity with Applications in Physics
Abstract: In this lecture the conditions for well behaved functions be complete monotonic (CM) and of Bernstein type (B) are discussed with a tutorial view-point. These mathematical conditions are relevant for the response functions characterizing relaxation processes in linear viscoelastic and dielectric media. As pointed out by several authors, requiring CM is essential to ensure the montonically decay of the energy in isolated systems (as it appears reasonable from physical considerations). Here we summarize the results recently obtained by the author with some collaborators where the response functions are CM, mainly of the Mittag-Leffler type. Indeed the Mittag-Leffler functions are shown to be related to the classical dielectric models.
Brief Biography of the Speaker: Presently Francesco MAINARDI is a retired professor of Mathematical Physics from the University of Bologna (since November 2013) where he has taught this course since 40 years. Even if retired, he continues to carry out teaching and research activity. His fields of research concern several topics of applied mathematics, including diffusion and wave problems, asymptotic methods, integral transforms, special functions, fractional calculus and non-Gaussian stochastic processes.
At present his H-index is > 50. For a full biography, list of references on author's papers and books see: Home