Heat kernels and function theory on metric measure spaces

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Eigenvalues of elliptic operators and geometric applications (2004, background): “See also [25] for function theory on fractal spaces.”
Diffusion polynomial frames on metric measure spaces (2008, background): “Thus, finite speed of wave propagation does not hold for certain fractal domains considered by Grigor’yan [19].”
A Quadrature Formula for Diffusion Polynomials Corresponding to a Generalized Heat Kernel (2010, unknown): “In [16], Grigor’yan has proved that (2.”
Estimates of heat kernels for non-local regular Dirichlet forms (2014, unknown): “2) pt (x, y) 1 tα/β ( 1 + d (x, y) t1/β )−(α+β′) , where β′ = βγ (see, for example, [13], [26], [36]).”