6533b85efe1ef96bd12bfe8d

RESEARCH PRODUCT

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

Camillo TrapaniJean-pierre Antoine

subject

rigged Hilbert space; generalized eigenvectors; simple spectrumrigged Hilbert spaceSettore MAT/05 - Analisi MatematicaGeneral Mathematicsgeneralized eigenvectorComputer Science (miscellaneous)simple spectrumEngineering (miscellaneous)Settore MAT/07 - Fisica Matematica

description

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.

yearjournalcountryeditionlanguage
2022-12-30Mathematics; Volume 11; Issue 1; Pages: 195
10.3390/math11010195https://dx.doi.org/10.3390/math11010195