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

被引：2
|
作者：
Antoine, Jean-Pierre [1 ]
Trapani, Camillo [2 ]
机构：
[1] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain la Neuve, Belgium
[2] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy
来源：
MATHEMATICS | 2023年 / 11卷 / 01期
关键词：
rigged Hilbert space; generalized eigenvectors; simple spectrum; QUANTUM-MECHANICS; SYMMETRY PROBLEMS; DIRAC FORMALISM;
D O I：
10.3390/math11010195
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页数：11
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