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The Laplacian matrix is the representation of a graph in matrix form.

5 votes
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190 views

Hilbert Modular Surface: Eigenfunctions of The Laplacian

The spectrum of the Laplacian on $L^2$ of a Hilbert modular surface decomposes into a discrete part and a continuous part $[1/4,\infty)$. The continuous part contains eigenvalues $\geq 1/4$. …
7 votes
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346 views

Locally symmetric spaces: spectrum of the Laplacian

Let $M = \Gamma\backslash X$ denote a locally symmetric space of non-compact type and $\Delta$ the Laplacian on $L^2(M)$. …