Operators in Rigged Hilbert Spaces, Gel'fand bases and generalized eigenvalues
(2023) Mathematics — Vol. 2023, n° 11, p. 195 (2023)
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- Authors
Antoine, Jean-Pierre 
- et. al.
- Abstract
- Given a self-adjoint operator $A$ in a Hilbert space $\H$, we analyze its spectral behavior when it is expressed in terms of generalized eigenvectors. Using the formalism of Gel'fand distribution bases, we explore the conditions for the generalized eigenspaces to be one-dimensional, i.e. for $A$ to have a simple spectrum.
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Citations
Antoine, J.-P., & et al. (2023). Operators in Rigged Hilbert Spaces, Gel’fand bases and generalized eigenvalues. Mathematics, 2023(11), 195. https://doi.org/10.3390/math11010195 (Original work published 2023)