Un método de proyección espectral para operadores de Jacobi

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Abstract

Let H be the Jacobi operator Hu(n) = u(n - 1) + u(n + 1) + v(n)u(n), u(0) = 0 acting on l2(Z+) where the potential v is real and v(n] → 0 as n → ∞. Let P be the orthogonal projection onto a closed linear subspace ℒ ⊂ l2(Z+), In a recent paper E.B. Davies defines the second order spectrum Spec2 (H, ℒ) of H relative to ℒ as the set of z ∈ C such that the restriction to ℒ of the operator P(H - z] 2P is not invertible within the space ℒ. The present paper is devoted to study properties of Spec2 (H, ℒ} when ℒ is large but finite dimensional. Our particular interest is the connection between this set and the spectrum of H. In our main result we provide sharp bounds in terms of the potential v for the asymptotic behaviour of Spec2(H, ℒ) as ℒ increases towards l2(Z +).

Original languageSpanish
Pages (from-to)111-113
Number of pages3
JournalRevista Mexicana de Fisica
Volume49
Issue numberSuppl. 3
Publication statusPublished - Nov 2003

Keywords

  • Estimation of the spectrum
  • Non-self-adjoint projection methods
  • Spectral theory of Jacobi operators

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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