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When do Sobolev spaces form a Hilbert scale?


Author: Andreas Neubauer
Journal: Proc. Amer. Math. Soc. 103 (1988), 557-562
MSC: Primary 46E35; Secondary 46M35
DOI: https://doi.org/10.1090/S0002-9939-1988-0943084-9
MathSciNet review: 943084
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Abstract: In this paper we show that the usual Sobolev spaces $ {\left( {{H^s}\left( \Omega \right)} \right)_{s \in {\mathbf{R}}}}$ are no Hilbert scale in the sense of Krein-Petunin, if $ \Omega $ is an open bounded subset of $ {{\mathbf{R}}^n}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0943084-9
Article copyright: © Copyright 1988 American Mathematical Society

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