منابع مشابه
Hill Operators and Spectral Operators of Scalar
We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H = −d 2 /dx 2 + V in L 2 (R) to be a spectral operator of scalar type. The conditions demonstrate 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. R ´ ESUMÉ. Quand un op...
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Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at 0, known to hold for bounded scalar type spectral operators, are shown to naturally transfer to the unbounded case. Curiosity is the lust of the mind.
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It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.
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We derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrödinger operator) H = −d/dx + 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 ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1963
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1963.13.1289