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Bohr’S Formula For One-Dimensional Schrã–Dinger Operators Defined By Self-Similar Measures With Overlaps

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  • WEI TANG

    (School of Mathematics and Statistics, Hunan First Normal University, Changsha, Hunan 410205, P. R. China)

Abstract

We study Bohr’s formula for fractal Schrödinger operators on the half line. These fractal Schrödinger operators are defined by fractal measures with overlaps and a locally bounded potential that tends to infinity. We first derive an analog of Bohr’s formula for these Schrödinger operators under some suitable conditions. Then we demonstrate how this result can be applied to self-similar measures with overlaps, including the infinite Bernoulli convolution associated with the golden ratio, m-fold convolution of Cantor-type measures, and a family of graph-directed self-similar measures that are essentially of finite type.

Suggested Citation

  • Wei Tang, 2022. "Bohr’S Formula For One-Dimensional Schrã–Dinger Operators Defined By Self-Similar Measures With Overlaps," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-11, September.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:06:n:s0218348x22501237
    DOI: 10.1142/S0218348X22501237
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