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.