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.