Abstract
One might perhaps hope that all self-adjoint operators (in a separable Hilbert space) have an orthonormal basis of eigenvectors, but this is not the case.
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Bennewitz, C., Brown, M., Weikard, R. (2020). Abstract spectral theory. In: Spectral and Scattering Theory for Ordinary Differential Equations. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-59088-8_3
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DOI: https://doi.org/10.1007/978-3-030-59088-8_3
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