TY  - JOUR
ID  - Pchelintseva2008
LB  - Pchelintseva2008
AU  - Pchelintseva, Irina
TI  - A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices
ST  - A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 2
SP  - 137
EP  - 150
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.2.137
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.2.137
AB  - We consider self-adjoint unbounded Jacobi matrices with diagonal \(q_n = b_{n}n\) and off-diagonal entries \(\lambda_n = n\), where \(b_{n}\) is a \(2\)-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the operator is either purely absolutely continuous or discrete. We study the situation where the spectral phase transition occurs, namely the case of \(b_{1}b_{2} = 4\). The main motive of the paper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix. The pure point part of the spectrum is analyzed in detail.
KW  - Jacobi matrices
KW  - spectral phase transition
KW  - absolutely continuous spectrum
KW  - pure point spectrum
KW  - discrete spectrum
KW  - subordinacy theory
KW  - asymptotics of generalized eigenvectors
SN  - 1232-9274
ER  -