Eigenfunctions, Transfer Matrices, and Absolutely Continuous Spectrum of One-dimensional Schrödinger Operators
نویسندگان
چکیده
on L(R ) (and its half-line problem, H+, on L2(0,∞) with u(0) = 0 boundary conditions). We will focus on a new approach to the absolutely continuous spectrum σac(h) and, more generally, Σac(h), the essential support of the a.c. part of the spectral measures. What is new in our approach is that it relies on estimates on the transfer matrix, that is, the 2× 2 matrix TE(n,m) which takes (u(m+1) u(m) ) to (u(n+1) u(n) ) for solutions u of hu = Eu (in the continuum case use ( u′(x) u(x) ) instead of ( u(x+1) u(x) ) ). We let TE(n) ≡ TE(n, 0). For example, we will prove the following:
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تاریخ انتشار 2002