Laplacians on self-similar sets and their spectrum

Jun Kigami

*(University of Tokyo)*

10:00 am to 11:00 am, November 20th, 2015 Science Building A1510

__Abstract:__

I will first explain how one can define a self-similar quadratic forms, called resistance forms, on certain class of self-similar sets called post critically finite self-similar sets. The typical example is the Sierpinski gasket. Even on the Sierpinski gasket, we can obtain Laplacians with variety of self-similarities. Then introducing self-similar measures, we will construct :self-similar¡± Laplacians. Finally we are going to see the asymptotic behavior of the eigenvalues of the Laplacians and compare them with those from the ordinary Laplacians on domains of the Euclidean spaces.

The attached file is the figure of the Sierpinski gasket.

The attached file is the figure of the Sierpinski gasket.

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