The Arithmetic Version of the Frequency Transition Conjecture: New Proof and Generalization

Lingrui Ge; Jiangong You; Xin Zhao

doi:10.1007/s42543-021-00040-y

Peking Mathematical Journal ›› 2021, Vol. 5 ›› Issue (2) : 349 -364. DOI: 10.1007/s42543-021-00040-y

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The Arithmetic Version of the Frequency Transition Conjecture: New Proof and Generalization

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Abstract

The arithmetic version of the frequency transition conjecture for the almost Mathieu operators was recently proved by Jitomirskaya and Liu [34]. We give a new proof via reducibility theory and duality, which derives from the method developed in [22] (in fact it is a simplified version). This new proof is applicable to more general quasiperiodic operators.

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Lingrui Ge, Jiangong You, Xin Zhao. The Arithmetic Version of the Frequency Transition Conjecture: New Proof and Generalization. Peking Mathematical Journal, 2021, 5(2): 349-364 DOI:10.1007/s42543-021-00040-y