On the spectrum of periodic perturbations of certain unbounded Jacobi operators | Zendy

Jaouad Sahbani | Zendy

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On the spectrum of periodic perturbations of certain unbounded Jacobi operators

Author(s) -

Jaouad Sahbani

Publication year - 2016

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2016.36.6.807

Subject(s) - spectrum (functional analysis) , diagonal , mathematics , perturbation (astronomy) , operator (biology) , mathematical analysis , continuous spectrum , absolute continuity , pure mathematics , physics , geometry , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene

It is known that a purely off-diagonal Jacobi operator with coefficients \(a_n=n^{\alpha}\), \(\alpha\in(0,1]\), has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum

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