June 2023 ON SUMS OF SEMIBOUNDED CANTOR SETS
Jake Fillman, Sara H. Tidwell
Rocky Mountain J. Math. 53(3): 737-754 (June 2023). DOI: 10.1216/rmj.2023.53.737

Abstract

Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets and growth assumptions on the functions, the sums of such sets contain half-lines. We also give examples to show our criteria are sharp in suitable regimes.

Citation

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Jake Fillman. Sara H. Tidwell. "ON SUMS OF SEMIBOUNDED CANTOR SETS." Rocky Mountain J. Math. 53 (3) 737 - 754, June 2023. https://doi.org/10.1216/rmj.2023.53.737

Information

Received: 13 June 2022; Revised: 4 July 2022; Accepted: 14 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617909
zbMATH: 07731143
Digital Object Identifier: 10.1216/rmj.2023.53.737

Subjects:
Primary: 28A80 , 35J10
Secondary: 52C23

Keywords: Spectral theory , sums of Cantor sets , thickness

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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