Singular decomposition of a differential operator on a semiaxis
type: Item
instance of: scholarly article
title: Singular decomposition of a differential operator on a semiaxis
zbMATH Open document ID: 0820.47023
DOI: 10.1007/BF00973466
author: V. Pereyra
published in: Siberian Mathematical Journal
publication date: 1994-11-08T00:00:00Z
review text: Let \(A\) be an \(n\times n\)-matrix and let \(M_ 1\) be a \(k\times n\)-matrix \((1\leq k\leq n-1)\) with orthonormal rows: \(M_ 1 M^*_ 1= I_ k\). Define the operator \(T\) in the space \(L_ 2(\mathbb{R}_ +)\) by \[ D(T)= \{x\in W^ 1_ 2(\mathbb{R}_ +);\;M_ 1 x(0)= 0\},\;Tx(t)= \textstyle{{dx\over dt}} (t)- Ax(t),\;t\in \mathbb{R}_ +. \] The author proves that \(T\) can be represented as a product of three operators: an isometry, a diagonal nonnegative definite operator, and one more isometry.
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 652213
zbMATH Keywords: isometry
zbMATH Keywords: diagonal nonnegative definite operator
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
cites work: Singular numbers of a boundary-value problem on the halfline for a linear system of ordinary differential equations
cites work: Q5555880
cites work: Q5631649
full work available at URL: https://doi.org/10.1007/bf00973466
OpenAlex ID: W2064007740
description: scientific article; zbMATH DE number 652213