Bound States and the Szegő Condition for Jacobi Matrices and Schrödinger Operators
نویسندگان
چکیده
For Jacobi matrices with an 1⁄4 1þ ð 1Þan g; bn 1⁄4 ð 1Þbn g; we study bound states and the Szeg + o condition. We provide a new proof of Nevai’s result that if g4 2 ; the Szeg + o condition holds, which works also if one replaces ð 1Þ by cos ðmnÞ: We show that if a 1⁄4 0; ba0; and go1 2 ; the Szeg + o condition fails. We also show that if g 1⁄4 1; a and b are small enough (b þ 8a2o 1 24 will do), then the Jacobi matrix has finitely many bound states (for a 1⁄4 0; b large, it has infinitely many). r 2003 Elsevier Inc. All rights reserved.
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