Papers by Abdelkader Intissar
Advances in Mathematical Physics, 2011
This paper is devoted to the study of the chaotic properties of some specific backward shift unbo... more This paper is devoted to the study of the chaotic properties of some specific backward shift unbounded operatorsHp=A*pAP+1;p=0,1,…realized as differential operators in Bargmann space, whereAandA*are the standard Bose annihilation and creation operators such that[A,A*]=I.
Chaoticit� de l'op�rateur de Gribov dans l'espace de Bargmann
C R Acad Sci Ser I Math, 2000
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000
Reçu le 3 avril 2000, accepté après révision le 25 septembre 2000) Résumé. En s'inspirant du résu... more Reçu le 3 avril 2000, accepté après révision le 25 septembre 2000) Résumé. En s'inspirant du résultat de Gulisashvili et MacCluer [14] nous montrons que le cas limite de l'opérateur de Gribov est chaotique dans l'espace de Bargmann. Notre méthode peut être appliquée pour obtenir la chaoticité de l'opérateur d'annihilation dans son espace des vecteurs entiers.
In J. Math. Anal. App. 305. (2005), we have considered the Gribov operator\\ $H_{\lambda'} = ... more In J. Math. Anal. App. 305. (2005), we have considered the Gribov operator\\ $H_{\lambda'} = \lambda' S + H_{\mu,\lambda}$ acting on Bargmann space where $ S = a^{*2} a^{2}$ and $ H_{\mu,\lambda} =\mu a^* a + \\i \lambda a^* (a+a^*)a$ with $i^{2} = -1$.\\ Here $a$ and $a^{*}$ are the standard Bose annihilation and creation operators satisfying the commutation relation $[a, a^{*}] = I$. In Reggeon field theory, the real parameters $\lambda{'}$ is the four coupling of Pomeron, $\mu$ is Pomeron intercept, $\lambda$ is the triple coupling of Pomeron and $i^{2} = -1$.\\ We have given an approximation of the semigroup $e^{-tH_{\lambda'}}$ generated by the operator $H_{\lambda'}$. In particulary, we have obtained an estimate approximation in trace norm of this semigroup by the unperturbed semigroup $e^{-t\lambda'S}$. In {\bf[12]}, we have regularized the operator $H_{\mu,\lambda}$ by $\lambda''G$ where $G = a^{*3} a^{3}$, i.e we have considered $H_{\lambda&#...
Analyse fonctionnelle et théorie spectrale pour les opérateurs compacts non auto-adjoints avec exercices et solutions (1997)
ABSTRACT L'étude spectrale des opérateurs linéaires non auto-adjoints est le point centra... more ABSTRACT L'étude spectrale des opérateurs linéaires non auto-adjoints est le point central de cet ouvrage. En particulier, une grande attention est portée à la présentation de certains critères de complétude des vecteurs propres généralisés des opérateurs non auto-adjoints compacts ou à résolvante compacte. Ce livre s'adresse aux étudiants des universités (2e et 3e cycle) ainsi qu'aux enseignants et chercheurs en mathématiques et sciences physiques.
Quelques nouvelles propriétés spectrales de l'hamiltonien de la théorie des champs de reggeons
Comptes Rendus De L Academie Des Sciences Serie 1 Mathematique, 1989
On considère le Hamiltonien de la théorie des champs de reggeons $H_{\alpha} = H_{0} + \alpha.H_{... more On considère le Hamiltonien de la théorie des champs de reggeons $H_{\alpha} = H_{0} + \alpha.H_{I}$ à n sites avec: $H_{0} = \sum_{j=1}^{n} \lambda'A_{j}^{*2}A_{j}^{2} + \muA_{j}^{*}A_{j} + i\lambda A_{j}^{*}(A_{j} + A_{j}^{*})A_{j} $. et $H_{I} = \sum_{j=1}^{n-1} A_{j+1}^{*}A_{j} + A_{j}^{*}A_{j+1} $. On montre par une méthode de perturbation que la plus petite valeur propre de cet opérateur est analytique en $\alpha$.
Etude spectrale d'une famiHe d'op~rateurs non-sym~triques intervenant dans la th~orie des champs de reggeons
Commun Math Phys, 1987
Mathematica, Aug 2, 2013
This article is devoted to the study of the chaotic properties of some specific bakward shift unb... more This article is devoted to the study of the chaotic properties of some specific bakward shift unbounded operators H p = z p D p+1 ; p = 0, 1, ..... realized as differential operators in generalized Fock-Bargmann spaces where D is the adjoint of the operator of multiplication by the independent variable z on generalized Fock-Bargmann spaces.
Spectral properties of the Cauchy transform on L2(C,e-|z|2lambda(z))
J Math Anal Appl, 2006
... Mathématiques Pures et Appliquées, Université des Sciences et Technologie de Lille I, 59655 V... more ... Mathématiques Pures et Appliquées, Université des Sciences et Technologie de Lille I, 59655 Villeneuve d'Ascq, France Received 5 August 2003 Available online 4 November 2005 Submitted by William F. Ames ... Acknowledgments The authors thank Jean-Karim and Soufiane. ...
Journal of Mathematical Analysis and Applications, May 1, 2001
Analyse de Scattering d'un Op�rateur Cubique de Heun dans l'Espace de Bargmann
Commun Math Phys, 1998
Quelques propriétés spectrales de l'hamiltonien de la théorie des champs de reggeons
Comptes Rendus De L Academie Des Sciences Serie 1 Mathematique, 1987
ABSTRACT Quelques propriétés spectrales de l'hamiltonien polynomial engendrant la théorie... more ABSTRACT Quelques propriétés spectrales de l'hamiltonien polynomial engendrant la théorie des reggeons
Mathematica, Jun 20, 2014
This article is devoted to build the nonlinear coherent states associated to the some specific ba... more This article is devoted to build the nonlinear coherent states associated to the some specific bakward shift unbounded operators H p = A * p A p+1 ; p = 0, 1, ..... realized as differential operators in classical Bargmann space where A and A * are the standard Bose annihilation and creation operators such that [A, A * ] = I. We use the Gazeau-Klauder formalism to construct the coherent states of this operator H p and investigate some properties of these coherent states.
Sur une propriété spectrale d’un opérateur non symétrique intervenant dans la théorie de Regge
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Diagonalisation of non selfadjoint operators arising in Gribov's reggeon theory
Comptes Rendus Mathematique
In this Note and the next ([5] and [6]) are a summary of our on going research on Gribov's re... more In this Note and the next ([5] and [6]) are a summary of our on going research on Gribov's reggeon theory. We consider the operator $H = \lambda'A*^{2}A^{2} + \muA*A + i\lambda.A*(A+A*)A$ where $A*$ and $A$ are the creation and annihilation opertors. Following the study done in [7], we prove that for $\lamda'^{2} \leq \mu\lambda' + \lambda^{2}$, the solutions of the equations $u'(t) + Hu(t) = 0$ are expandible in series of the eigenvectors of $H$ for $ t > 0$.
Quelques nouvelles proriétés spectrales de l’hamiltonien de la théorie des champs de reggeous. (A few new spectral properties of the Hamiltonian of reggeon field theory)
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
Complex Analysis and Operator Theory, 2015
On the chaoticity of some tensor product weighted backward shift operators acting on some tensor ... more On the chaoticity of some tensor product weighted backward shift operators acting on some tensor product Fock-Bargmann spaces Abdelkader INTISSAR (*) (* *)
A short note on the chaoticity of a weight shift on concrete orthonormal basis associated to some Fock-Bargmann space
Journal of Mathematical Physics, 2014
ABSTRACT In this work [J. Math. Phys. 55, 0011502 (2014)], we give a concrete example of chaotic ... more ABSTRACT In this work [J. Math. Phys. 55, 0011502 (2014)], we give a concrete example of chaotic weighted shift acting on theta Fock-Bargmann space recently constructed by Ghanmi-Intissar [J. Math. Phys. 54, 063514 (2013)].
Journal of Mathematical Analysis and Applications, 2005
The Reggeon field theory is governed by a non-self adjoint operator constructed as a polynomial i... more The Reggeon field theory is governed by a non-self adjoint operator constructed as a polynomial in A, A * , the standard Bose annihilation and creation operators. In zero transverse dimension, this Hamiltonian acting in Bargmann space is defined by H λ ,µ = λ A * 2 A 2 + µA * A + iλA * A * + A A, where i 2 = −1, λ , µ and λ are real numbers and the operators A, A * satisfy the commutation relation [A, A * ] = I. As the quantum mechanical system described by H λ ,µ has a velocity-dependent potential containing powers of momentum up to the fourth, the problem of existence of Hamiltonian path integral for the evolution operator e −tH λ ,µ of this theory is of interest on its own. In particular, can we express e −tH λ ,µ as a limit of "integral" operators? In this article one considerably reduces the difficulty by studying the Trotter product formula of H λ ,µ to reach two objectives: • The first objective is to prove a very specific error estimate for the error in a Trotter product formula in trace-norm for H viewed as the sum of the operators λ A * 2 A 2 and µA * A + iλA * × (A * + A)A. • The second objective of this work is to give a approximation of the semigroup generated by H λ ,µ when H λ ,µ is split in the sum of λ A
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Papers by Abdelkader Intissar