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The operator $ ({\rm sgn}\,x)d\sp 2/dx\sp 2$ is similar to a selfadjoint operator in $ L\sp 2({\bf R})$


Authors: Branko Ćurgus and Branko Najman
Journal: Proc. Amer. Math. Soc. 123 (1995), 1125-1128
MSC: Primary 47B25; Secondary 34L05, 47B50, 47E05
DOI: https://doi.org/10.1090/S0002-9939-1995-1223513-X
MathSciNet review: 1223513
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Abstract: Krein space operator-theoretic methods are used to prove that the operator $ (\operatorname{sgn} x)\frac{{{d^2}}}{{d{x^2}}}$ is similar to a selfadjoint operator in the Hilbert space $ {L^2}({\mathbf{R}})$.


References [Enhancements On Off] (What's this?)

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  • [2] B. Ćurgus and H. Langer, A Krein space approach to symmetric ordinary differential operators with an indefinite weight function, J. Differential Equations 79 (1989), 31-61. MR 997608 (90j:47060)
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DOI: https://doi.org/10.1090/S0002-9939-1995-1223513-X
Article copyright: © Copyright 1995 American Mathematical Society

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