On an unconditional basis of generalized eigenvectors of the nonselfadjoint Gribov operator in Bargmann space
type: Item
instance of: scholarly article
title: On an unconditional basis of generalized eigenvectors of the nonselfadjoint Gribov operator in Bargmann space
zbMATH Open document ID: 0959.47013
author: Marie-Thérèse Aimar
author: Abdelkader Intissar
author: Aref Jeribi
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-04-20T00:00:00Z
review text: One of the attempts to understand strong interactions is governed by a nonselfadjoint Gribov operator constructed as a polynomial in \(A, A^{*},\) the standard Bose annihilation and creation operators. In the reviewed article it is proved that the system of generalized eigenvectors of the Gribov operator is an unconditional basis in Bargmann space. The authors give a generalized diagonalization in the Abel sense of the semigroups assiciated to Gribov operator and to its square root.
Mathematics Subject Classification ID: 47A70
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1274908
zbMATH Keywords: Regge fields theory
zbMATH Keywords: Gribov operator
zbMATH Keywords: Bargmann space
zbMATH Keywords: unconditional basis
zbMATH Keywords: strong interactions
zbMATH Keywords: Bose annihilation and creation operators
zbMATH Keywords: system of generalized eigenvectors
zbMATH Keywords: diagonalization
zbMATH Keywords: square root
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6258
OpenAlex ID: W2015674011
cites work: Q4022197
cites work: Density of generalized eigenvectors of a class of compact nonselfadjoint operators and applications
cites work: Q4850418
cites work: Some new regularity properties for Gribov's operator
cites work: Critères de complétude des vecteurs propres généralisés d'une classe d'opérateurs non auto-adjoints compacts ou à résolvante compacte et applications
cites work: Sur une valeur propre d'un opérateur
cites work: REMARKS ON A HILBERT SPACE OF ANALYTIC FUNCTIONS
cites work: Q5336643
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: Q1103163
cites work: Q4534679
cites work: Q4735652
cites work: Scattering analysis of the cubic Heun operator in Bargmann space
cites work: Q5526485
cites work: Q3775869
cites work: Summability of series in the principal vectors of non-self adjoint operators
cites work: Q3994769
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Multiple completeness of a system of characteristic and adjoined elements of a polynomial operator bundle and multiple decompositions with respect to this system
DOI: 10.1006/JMAA.1998.6258
description: scientific article; zbMATH DE number 1274908