75 citations · 932 across the 61 of their papers we have counts for
8 papers · 1 filter
Closability, regularity, and approximation by graphs for separable bilinear forms
Michael Hinz, Alexander Teplyaev
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic fo…
Singularly continuous spectrum of a self-similar Laplacian on the half-line
Joe P. Chen, Alexander Teplyaev
We investigate the spectrum of the self-similar Laplacian, which generates the so-called " random walk" on the integer half-line . Using the method of spectral de…
Fractal AC circuits and propagating waves on fractals
Eric Akkermans, Joe P. Chen, Gerald Dunne +2
We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the in…
Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials
Ulysses Andrews, Grigory Bonik, Joe P. Chen +2
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation t…
Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
Joe P. Chen, Stanislav Molchanov, Alexander Teplyaev
We establish an asymptotic formulas for the eigenvalue counting function of the Schrödinger operator for some unbounded potentials on several types of unbounded fractal…
Dual graphs and modified Barlow--Bass resistance estimates for repeated barycentric subdivisions
Daniel J. Kelleher, Antoni Brzoska, Hugo Panzo +1
We prove Barlow--Bass type resistance estimates for two random walks associated with repeated barycentric subdivisions of a triangle. If the random walk jumps between the centers o…