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Some jacobi matrices with decaying potential and dense point spectrum

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Abstract

We discuss doubly infinite matrices of the formM ij=δ i,j+1+δ i,j−1+V iδ ij as operators on ℓ2. We present for each ɛ>0, examples of potentialsV n with |V n|=O(n −1/2+ɛ) and whereM has only point spectrum. Our discussion should be viewed as a remark on the recent work of Delyon, Kunz, and Souillard.

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Authors and Affiliations

  1. Departments of Mathematics and Physics, California Institute of Technology, 91125, Pasadena, CA, USA

    Barry Simon

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  1. Barry Simon
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Communicated by T. Spencer

Research partially supported by USNSF under grant MCS 81-20833

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Simon, B. Some jacobi matrices with decaying potential and dense point spectrum. Commun.Math. Phys. 87, 253–258 (1982). https://doi.org/10.1007/BF01218563

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  • DOI: https://doi.org/10.1007/BF01218563

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