Norm estimates of discrete Schrödinger operators
Szwarc, Ryszard
Colloquium Mathematicae, Tome 78 (1998), p. 153-160 / Harvested from The Polish Digital Mathematics Library
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Harper’s operator is defined on ℓ2(Z) by Hθξ(n)=ξ(n+1)+ξ(n-1)+2cosnθξ(n), where θ∈[0,π]. We show that the norm of ∥Hθ∥ is less than or equal to 22 for π/2≤θ≤π. This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:210547 
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     author = {Ryszard Szwarc},
     title = {Norm estimates of discrete Schr\"odinger operators},
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     volume = {78},
     year = {1998},
     pages = {153-160},
     zbl = {0904.47025},
     language = {en},
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Szwarc, Ryszard. Norm estimates of discrete Schrödinger operators. Colloquium Mathematicae, Tome 78 (1998) pp. 153-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv76z1p153bwm/

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