Essential spectrum and L(2)-solutions of one-dimensional Schrodinger operators

Autor(en): Remling, C
Stichwörter: essential spectrum; Hartman-Wintner conjecture; inverse spectral theory; L(2)-solution; Mathematics; Mathematics, Applied; one-dimensional Schrodinger operator
Erscheinungsdatum: 1996
Herausgeber: AMER MATHEMATICAL SOC
Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 124
Ausgabe: 7
Startseite: 2097
Seitenende: 2100
Zusammenfassung: 
In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrodinger operator possess square integrable solutions, then the essential spectrum is' nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrodinger operators which satisfy the condition of existence of L(2)-solutions. The proof of this theorem is based on inverse spectral theory.
ISSN: 00029939
DOI: 10.1090/S0002-9939-96-03463-6

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