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Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces | | Joe P. Chen
; Stanislav Molchanov
; Alexander Teplyaev
; | | Date: |
15 May 2015 | | Abstract: | We establish an asymptotic formulas for the eigenvalue counting function of
the Schr"odinger operator $-Delta +V$ 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. | | Source: | arXiv, 1505.3923 | | Services: | Forum | Review | PDF | Favorites | |
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