  The main difference between certain spectral problems for linear
Schr\"odinger operators, e.g. the almost Mathieu equation, and three-term
recurrence relations for orthogonal polynomials is that in the former the index
ranges across $\ZZ$ and in the latter only across $\Zp$. We present a technique
that, by a mixture of Dirichlet and Taylor expansions, translates the almost
Mathieu equation and its generalizations to three term recurrence relations.
This opens up the possibility of exploiting the full power of the theory of
orthogonal polynomials in the analysis of Schr\"odinger spectra.
  Aforementioned three-term recurrence relations share the property that their
coefficients are almost periodic. We generalize a method of proof, due
originally to Jeff Geronimo and Walter van Assche, to investigate essential
support of the Borel measure of associated orthogonal polynomials, thereby
deriving information on the underlying absolutely continuous spectra of
Schr\"odinger operators.
