7月5日(木) 15:00 -- 16:30 梶野 直孝(京都大学情報学研究科) ``The spectral counting function on self-similar sets: its relation with the geometric counting function and the Weyl-type asymptotics'' <研究発表要旨> Given a self-similar Dirichlet form on a self-similar set, we study a relation between the eigenvalue counting function of the Laplacian associated with the Dirichlet form and the geometric counting function with respect to a proper family of coverings of the self-similar set. We also deduce Weyl's asymptotic behavior of the eigenvalue counting function of the non-negative self-adjoint operator associated with the Dirichlet form, when the underlying measure is a self-similar measure, by assuming the (sub-)Gaussian heat kernel upper bound and a condition on topological structure of the boundary of the self-similar set. We show, at the presentation, our results through the case of Sierpinski carpets.