Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
Chen, Joe P. · Molchanov, Stanislav · Teplyaev, Alexander
Original · EN
We establish an asymptotic formulas for the eigenvalue counting function of the Schrödinger operator -Δ+V for some unbounded potentials V on several types of unbounded fractal spaces. We give sufficient conditions for Bohr's formula to hold on metric measure spaces which admit a cellular decomposition, and then verify these conditions for fractafolds and fractal fields based on nested fractals. In particular, we partially answer a question of Fan, Khandker, and Strichartz regarding the spectral asymptotics of the harmonic oscillator potential on the infinite blow-up of a Sierpinski gasket.
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