A comparison theorem for selfadjoint operators
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- by Amin Boumenir PDF
- Proc. Amer. Math. Soc. 111 (1991), 161-175 Request permission
Abstract:
In this work we shall establish a result concerning the spectral theory of differential operators. Let ${L_1}$ and ${L_2}$ be two self-adjoint operators acting in two different Hubert spaces. Then under some conditions we shall prove that \[ (d{\Gamma _1}/d{\Gamma _2})({L_2}) = \overline V V’,\] where ${\Gamma _1}(\lambda )$ and ${\Gamma _2}(\lambda )$ are the spectral functions associated with ${L_1}$ and ${L_2}$ respectively. $V$ is the shift operator mapping the set of generalized eigenfunctions of ${L_1}$ into the set of generalized eigenfunctions of ${L_2}$, that is \[ y = V\varphi ,\] where ${L_2}y = \lambda y$ and ${L_1}\varphi = \lambda \varphi$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 161-175
- MSC: Primary 47B25; Secondary 34L40, 47A70, 47E05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1021896-3
- MathSciNet review: 1021896