The absolutely continuous spectrum of discrete canonical systems

Fischer, Andreas; Remling, Christian

doi:10.1090/S0002-9947-08-04711-9

The absolutely continuous spectrum of discrete canonical systems
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by Andreas Fischer and Christian Remling PDF

Trans. Amer. Math. Soc. 361 (2009), 793-818 Request permission

Abstract:

We prove that if the canonical system $J(y_{n+1}-y_n)= zH_ny_n$ has absolutely continuous spectrum of a certain multiplicity, then there is a corresponding number of linearly independent solutions $y$ which are bounded in a weak sense.

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