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

页数：11

共 50 条

[31] INVERSE PROBLEM FOR SELF-ADJOINT OPERATORS ON A TENSOR PRODUCT OF RIGGED HILBERT SPACES
BUTLER, JB
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (03): : A349 - A349
[32] Eigenvalues of Generalized Shift Operators Over lp(τ) Spaces
Hajiabootorabi, Mahin
Mardanbeigi, Mohammad Reza
IRANIAN JOURNAL OF SCIENCE, 2024, 48 (05) : 1265 - 1270
[33] A SPECTRAL THEORY OF LINEAR OPERATORS ON RIGGED HILBERT SPACES UNDER ANALYTICITY CONDITIONS II: APPLICATIONS TO SCHRODINGER OPERATORS
Chiba, Hayato
KYUSHU JOURNAL OF MATHEMATICS, 2018, 72 (02) : 375 - 405
[34] Rigged Hilbert spaces for chaotic dynamical systems
Suchanecki, Z
Antoniou, I
Tasaki, S
Bandtlow, OF
JOURNAL OF MATHEMATICAL PHYSICS, 1996, 37 (11) : 5837 - 5847
[35] Groups, Special Functions and Rigged Hilbert Spaces
Celeghini, Enrico
Gadella, Manuel
del Olmo, Mariano A.
AXIOMS, 2019, 8 (03)
[36] Perturbation of generalized inverses of linear operators in Hilbert spaces
J Math Anal Appl, 2 (506):
[37] Groups, Jacobi functions, and rigged Hilbert spaces
Celeghini, E.
Gadella, M.
del Olmo, M. A.
JOURNAL OF MATHEMATICAL PHYSICS, 2020, 61 (03)
[38] ENCLOSING EIGENVALUES OF COMPLETELY CONTINUOUS POSITIVE OPERATORS IN SEPARABLE HILBERT SPACES
DIRSCHMID, H
COMPUTING, 1970, 5 (02) : 119 - +
[39] Generalized numerical radius inequalities of operators in Hilbert spaces
Kais Feki
Advances in Operator Theory, 2021, 6
[40] Some New Notions of Bases for the Range of Operators in Hilbert Spaces
Hosseinnezhad, Hessam
SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2024, 21 (03): : 249 - 266

← 1 2 3 4 5 →