As picture below, what is the mean of $L^2(R^2, dxdy)$ and $L^2(H,y^{-2}dxdy)$ ? I know what is $L^2$ , but I don't know what is $dxdy$. Besides, how to get the equation 1 and 2 ?
Below picture is from this paper.
2026-04-07 07:28:55.1775546935
Proof of spectrum of Laplacian on hyperbolic plane.
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