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- W2076602752 abstract "We derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrö dinger operator) H = −d 2 /dx 2 + V to be a spectral operator of scalar type. The conditions show the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. In the course of our analysis, we also establish a functional model for periodic Schrödinger operators that are spectral operators of scalar type and develop the corresponding eigenfunction expansion. The problem of deciding which Hill operators are spectral operators of scalar type appears to have been open for about 40 years." @default.
- W2076602752 created "2016-06-24" @default.
- W2076602752 creator A5030354164 @default.
- W2076602752 creator A5053434924 @default.
- W2076602752 date "2009-01-01" @default.
- W2076602752 modified "2023-10-13" @default.
- W2076602752 title "A criterion for Hill operators to be spectral operators of scalar type" @default.
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- W2076602752 doi "https://doi.org/10.1007/s11854-009-0012-5" @default.
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