Certain indicators of the quasi-nilpotency of functional operators
type: Item
instance of: scholarly article
title: Certain indicators of the quasi-nilpotency of functional operators
zbMATH Open document ID: 0959.47001
author: V. I. Sumin
author: A. V. Chernov
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: This article presents some modifications of the theorem about the vanishing of the spectral radius of the linear Volterra operator \(G\) in \(L_\infty\) in terms of the existence of increasing chains \(\{H_0, H_1,\dots, H_k\}\) of invariant subspaces such that \(\|P_{H_i/H_{i-1}}\|< \delta\), \(i= 1,\dots, k\). These modifications are applied to the study of the linear operator with partial integrals; this operator arises the Riemann problem for the equation \[ x_{t^1t^2}= f(t,x(t), x_{t^1}(t), x_{t^2}(t))\qquad (t\in \mathbb{R}^2) \] in a special domain.
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1541575
zbMATH Keywords: spectral radius
zbMATH Keywords: linear Volterra operator
zbMATH Keywords: invariant subspaces
zbMATH Keywords: partial integrals
zbMATH Keywords: Riemann problem
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541575