The Decimation Method for Laplacians on Self-Similar Fractals and Their Spectral Zeta Functions

Start: 12/05/2012 - 4:15pm
End  : 12/05/2012 - 5:15pm


Nishu Lal (Scripps College)


We construct the second order differential operator called the Laplacian on the bounded Sierpin- ski gasket and discuss its spectral properties. The decimation method is a process through which the spectrum of the Laplace operator can be related to the dynamics of the iteration of a certain polynomial on C. Furthermore, we discuss the spectral zeta function of the Laplacians on the bounded Sierpinski gasket and its blowup, known as the unbounded Sierpinski gasket. The spectral zeta function of the Laplacian on the unbounded Sierpinski gasket has a factorization formula expressed in terms of a suitable hyperfunction and the spectral zeta function associated with the bounded Sierpinski gasket. Finally, we breify discuss the generalization of the decimation method and the factorization of the spectral zeta function to the multi-variable case, via the example of fractal Sturm–Liouville operators on the half-line.

Millikan 134, Pomona College

Lal-revised.pdf105.19 KB

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