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Weyl-type asymptotic formula for Schr\"odinger operators on unbounded fractal spaces

Wei Tang Zhiyong Wang

Analysis of PDEs mathscidoc:2211.03001

2022.2
We study an asymptotic estimate on the number of negative eigenvalues of the Schr\"odinger operators on unbounded fractal spaces which admit a cellular decomposition. We first give some sufficient conditions for Weyl-type asymptotic formula to hold. Second, we verify these conditions for the infinite blowup of Sierpi\'nski gasket and unbounded generalized Sierpi\'nski carpets. Final, we demonstrate how the result can be applied to the infinite blowup of certain fractals associated with iterated function systems with overlaps, including those defining the classical infinite Bernoulli convolution with golden ratio.
Fractal; Schrodinger operator; Laplacian; self-similar measure with overlaps
[ Download ] [ 2022-11-05 21:50:14 uploaded by WeiTang ] [ 2109 downloads ] [ 0 comments ] 
@inproceedings{wei2022weyl-type,
  title={Weyl-type asymptotic formula for Schr\"odinger operators on unbounded fractal spaces},
  author={Wei Tang, and Zhiyong Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20221105215014519210736},
  year={2022},
}
Wei Tang, and Zhiyong Wang. Weyl-type asymptotic formula for Schr\"odinger operators on unbounded fractal spaces. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20221105215014519210736.
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