BOHR’S FORMULA FOR ONE-DIMENSIONAL SCHRÖDINGER OPERATORS DEFINED BY SELF-SIMILAR MEASURES WITH OVERLAPS

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

FRACTALS (fractals), 2022, vol. 30, issue 06, 1-11

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.

Keywords: Fractal; Schrödinger Operator; Bohr’s Formula; Laplacian; Self-Similar Measure with Overlaps (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501237

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