96-394 Gerald Teschl

Spectral Deformations of Jacobi Operators (35K, LaTeX2e) Sep 2, 96

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Abstract. We extend recent work concerning isospectral deformations for one-dimensional Schr\"odinger operators to the case of Jacobi operators. We provide a complete spectral characterization of a new method that constructs isospectral deformations of a given Jacobi operator $(H u)(n) = a(n) u(n+1) + a(n-1) u(n-1) - b(n) u(n)$. Our technique is connected to Dirichlet data, that is, the spectrum of the operator $H^\infty_{n_0}$ on $\ell^2 (-\infty,n_0) \oplus \ell^2 (n_0,\infty)$ with a Dirichlet boundary condition at $n_0$. The transformation moves a single eigenvalue of $H^\infty_{n_0}$ and perhaps flips which side of $n_0$ the eigenvalue lives. On the remainder of the spectrum the transformation is realized by a unitary operator.

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