Natural boundaries and spectral theory

J. Breuer Jonathan; B. Simon Barry

doi:10.1016/j.aim.2010.12.019

Natural boundaries and spectral theory

J. Breuer Jonathan, B. Simon Barry

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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 language	English
Pages (from-to)	4902-4920
Number of pages	19
Journal	Advances in Mathematics
Volume	226
Issue number	6
DOIs	https://doi.org/10.1016/j.aim.2010.12.019
State	Published - 1 Apr 2011

Bibliographical note

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

Keywords

30B20
30B30
35P05
Natural boundary
Reflectionless
Right limit

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10.1016/j.aim.2010.12.019

Cite this

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abstract = "We present and exploit an analogy between lack of absolutely continuous spectrum for Schr{\"o}dinger 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.",

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author = "{Breuer Jonathan}, J. and {Simon Barry}, B.",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (J. Breuer), [email protected] (B. Simon). 1 Supported in part by NSF grant DMS-0652919.",

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KW - 35P05

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KW - Reflectionless

KW - Right limit

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Natural boundaries and spectral theory

Abstract

Bibliographical note

Keywords

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