We present and exploit an analogy between lack of absolutely continuous spectrum for Schrödinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke's example and natural boundary examples for random power series where independence is not assumed.
Bibliographical noteFunding Information:
* Corresponding author. E-mail addresses: firstname.lastname@example.org (J. Breuer), email@example.com (B. Simon). 1 Supported in part by NSF grant DMS-0652919.
- Natural boundary
- Right limit