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.
引用
收藏
页数：11
相关论文
共 50 条
  • [1] Singular Perturbations and Operators in Rigged Hilbert Spaces
    Salvatore di Bella
    Camillo Trapani
    Mediterranean Journal of Mathematics, 2016, 13 : 2011 - 2024
  • [2] Singular Perturbations and Operators in Rigged Hilbert Spaces
    di Bella, Salvatore
    Trapani, Camillo
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (04) : 2011 - 2024
  • [3] Partial multiplication of operators in rigged Hilbert spaces
    Trapani, C
    Tschinke, F
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2005, 51 (04) : 583 - 600
  • [4] Partial Multiplication of Operators in Rigged Hilbert Spaces
    Camillo Trapani
    Francesco Tschinke
    Integral Equations and Operator Theory, 2005, 51 : 583 - 600
  • [5] Riesz-Like Bases in Rigged Hilbert Spaces
    Bellomonte, Giorgia
    Trapani, Camillo
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2016, 35 (03): : 243 - 265
  • [6] Operators in rigged Hilbert spaces: Some spectral properties
    Bellomonte, Giorgia
    Di Bella, Salvatore
    Trapani, Camillo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 411 (02) : 931 - 946
  • [7] Levy-Laplace operators in functional rigged Hilbert spaces
    Accardi, L
    Smolyanov, OG
    MATHEMATICAL NOTES, 2002, 72 (1-2) : 129 - 134
  • [8] Application of the Rigged Hilbert Spaces into the Generalized Signals & Systems Theory
    Heredia-Juesas, J.
    Gago-Ribas, E.
    Vidal-Garcia, P.
    PROCEEDINGS OF THE 2015 INTERNATIONAL CONFERENCE ON ELECTROMAGNETICS IN ADVANCED APPLICATIONS (ICEAA), 2015, : 1365 - 1368
  • [9] Rigged Hilbert spaces and contractive families of Hilbert spaces
    Bellomonte, Giorgia
    Trapani, Camillo
    MONATSHEFTE FUR MATHEMATIK, 2011, 164 (03): : 271 - 285
  • [10] Rigged Hilbert spaces and contractive families of Hilbert spaces
    Giorgia Bellomonte
    Camillo Trapani
    Monatshefte für Mathematik, 2011, 164 : 271 - 285
12345