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Operators in Rigged Hilbert Spaces, Gel’fand Bases and Generalized Eigenvalues

2022

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.

rigged Hilbert space; generalized eigenvectors; simple spectrumrigged Hilbert spaceSettore MAT/05 - Analisi MatematicaGeneral Mathematicsgeneralized eigenvectorComputer Science (miscellaneous)simple spectrumEngineering (miscellaneous)Settore MAT/07 - Fisica MatematicaMathematics; Volume 11; Issue 1; Pages: 195
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