Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging

  • Jan Janas
  • Serguei Naboko
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 117)


We consider unbounded, selfadjoint Jacobi matrices with weights λ n = n α(1+Δ n ), LimΔ n =0 and α \(\alpha \in (\frac{1} {2},1)\). The asymptotics for generalized eigenvectors of fixed energy is obtained. This allows to carry out, by using so called grouping in block method, analysis of absolutely continuous spectra of our class of operators. The main role play here algebraic properties of Pauli matrices arising in natural way in the analysis of corresponding transfer matrices. It happenes that the commutation relations between Pauli matrices lead to the appearance of Cesaro-like averages in our study.


Continuous Spectrum Pauli Matrice Absolute Continuity Jacobi Matrice Block Method 
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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • Jan Janas
    • 1
  • Serguei Naboko
    • 2
  1. 1.Institute of MathematicsPolish Academy of Sciences Cracow BranchKrakówPoland
  2. 2.Department of Mathematical Physics, Institute of PhysicsSt. Petersburg UniversitySt. Petergoff, S.-PetersburgRussia

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