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Heat kernels for the Bessel operator

Le : 16/04/2018 11h00
Par : Kamil Bogus (Wrocław University)
Lieu : i103
Lien web :
Résumé : I will present the main results of my PhD thesis. The talk will be divided into two parts. In the first part, I will consider the Dirichlet heat kernels in half-lines for the Bessel differential operator. In particular, I provide the sharp, two-sided estimates and asymptotic expansions of the considered heat kernels. The main advantage of this results is that the exponential behaviour is described explicitly i.e. there are the same constants in the upper and lower bound. Such precise results are very exceptional in the theory of partial differential equations as well as in the theory of stochastic processes. In the second part, I will move to the applications of the above-mentioned results to the potential theory on real hyperbolic space. Namely, I present a formula connecting Bessel heat kernels and the Green function of a half-space. Moreover, I provide the sharp, two-sided estimates of the mentioned Green function.