Estimates for negative eigenvalues of Schrödinger operators on unbounded fractal spaces

Tang, Wei; Wang, Zhiyong

doi:10.1090/tran/9005

Estimates for negative eigenvalues of Schrödinger operators on unbounded fractal spaces
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by Wei Tang and Zhiyong Wang;

Trans. Amer. Math. Soc. 377 (2024), 697-730

DOI: https://doi.org/10.1090/tran/9005

Published electronically: October 6, 2023

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Abstract:

We study an asymptotic formula for the number of negative eigenvalues of Schrödinger 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 Sierpiński gasket and unbounded generalized Sierpiński carpets. Finally, 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.

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