6 citations · 8 across the 4 of their papers we have counts for
4 papers
Local and Non-Local Dirichlet Forms on the Sierpiński Carpet
Alexander Grigor'yan, Meng Yang
We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpiński carpet using approximation of stable-like non-local closed forms which gives…
Determination of the Walk Dimension of the Sierpiński Gasket Without Using Diffusion
Alexander Grigor'yan, Meng Yang
We determine the walk dimension of the Sierpiński gasket without using diffusion. We construct non-local regular Dirichlet forms on the Sierpiński gasket from regular Dirichlet for…
A lower bound for the number of negative eigenvalues of Schrödinger operators
Alexander Grigor'yan, Nikolai Nadirashvili, Yannick Sire
We prove a lower bound for the number of negative eigenvalues for a Schrödinger operator on a Riemannian manifold via the integral of the potential.
Negative eigenvalues of two-dimensional Schrödinger operators
Alexander Grigor'yan, Nikolai Nadirashvili
We prove a certain upper bound for the number of negative eigenvalues of the Schrödinger operator on the plane.