On regularized trace formula of Gribov semigroup generated by the Hamiltonian of Reggeon field theory in Bargmann representation
type: Item
instance of: scholarly article
title: On regularized trace formula of Gribov semigroup generated by the Hamiltonian of Reggeon field theory in Bargmann representation
zbMATH Open document ID: 1387.43007
author: Abdelkader Intissar
author: Jean-Karim Intissar
author: Marie-Thérèse Aimar
published in: Complex Analysis and Operator Theory
publication date: 2018-04-16T00:00:00Z
review text: Suppose \({\mathbb E}\) is the Bargmann space of all entire functions \(f:{\mathbb C}\to {\mathbb C}\) such that \(\int_{\mathbb C}|f(z)|^2e^{-|z|^2}\,dx\,dy<\infty\). Let \({\mathbb H}_{\lambda''}=\lambda''{\mathbb G}+{\mathbb H}_{\mu,\lambda}\) be the Gribov operator acting on \({\mathbb E}\), where \({\mathbb G}=a^{*3}a^3\), \(a\) and its adjoint \(a^*\) are annihilation and creation operators, respectively, satisfying \([a,a^*]={\mathbb I}\), and \({\mathbb H}_{\mu,\lambda}=\mu a^*a+i\lambda a^*(a+a^*)a\). Here \(\lambda'',\mu,\lambda\) are real parameters and \(i^2=-1\). Let \(\|\cdot\|_1\) denote the trace-class norm. The main result of the paper is the following asymptotic formula: \(\big\|e^{-t{\mathbb H}_{\lambda''}}-e^{-t\lambda''{\mathbb G}}\big\|_1= t\big\|e^{-t\lambda''{\mathbb G}}{\mathbb H}_{\mu,\lambda}\big\|_1+ \big\| (\lambda''{\mathbb G})^{\delta} e^{-\frac{t}{3}\lambda''{\mathbb G}} \big\|_1 O(t^2)\) as \(t\to 0^+\) for \(\delta\geq 1/2\).
reviewed by: Oleksiy Karlovych
Mathematics Subject Classification ID: 43A45
Mathematics Subject Classification ID: 47B32
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 32K15
Mathematics Subject Classification ID: 34L10
zbMATH DE Number: 6860216
zbMATH Keywords: non-self-adjoint linear operators
zbMATH Keywords: Gribov operator
zbMATH Keywords: regularized trace formula of Gribov operator
zbMATH Keywords: asymptotic expansion of trace of semigroups
zbMATH Keywords: regularized trace formula of Gribov semigroup
zbMATH Keywords: Bargmann space
zbMATH Keywords: Reggeon field theory
MaRDI profile type: Publication
full work available at URL: s11785-017-0707-z
OpenAlex ID: W2962786666
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DOI: 10.1007/S11785-017-0707-Z
description: scientific article; zbMATH DE number 6860216