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.
Antoine, J., Trapani, C. (2022). Operators in Rigged Hilbert Spaces, Gel’fand Bases and Generalized Eigenvalues. MATHEMATICS, 11(1), 195 [10.3390/math11010195].
Operators in Rigged Hilbert Spaces, Gel’fand Bases and Generalized Eigenvalues
Trapani, Camillo
2022-01-01
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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