Natural boundaries and spectral theory

J. Breuer Jonathan, B. Simon Barry

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageAmerican English
Pages (from-to)4902-4920
Number of pages19
JournalAdvances in Mathematics
Issue number6
StatePublished - 1 Apr 2011

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: (J. Breuer), (B. Simon). 1 Supported in part by NSF grant DMS-0652919.


  • 30B20
  • 30B30
  • 35P05
  • Natural boundary
  • Reflectionless
  • Right limit


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