Algebraic and differential operator equations
type: Item
instance of: scholarly article
title: Algebraic and differential operator equations
zbMATH Open document ID: 0658.34054
DOI: 10.1016/0024-3795(88)90319-9
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let H be a complex separable Hilbert space and let L(H) be the algebra of all bounded linear operators on H. The boundary value problem (1) \(X^{(n)}+A_{n-1}X^{(n-1)}+...+A_ 0X=0\), (2) \(EX(b)-X(0)F=G\), where \(A_ i,E,F,G\in L(H)\) and b is a positive real number is considered. Explicit expressions for solutions (in L(H)) of the BVP (1), (2) and the Cauchy problem for equation (1) are given in terms of solutions (in L(H)) of the algebraic equation (3) \(X^ n+A_{n- 1}X^{n-1}+...+A_ 0X=0.\) A method for solving equation (3) by reducing the degree of the equation is studied. This reduction is based on the application of annihilating analytic functions of operators. The paper can be regarded as a continuation of the recently author's paper ``Explicit solutions for second order operator differential equations with two boundary value conditions'' [Linear Algebra Appl. 103, 73-86 (1988)].
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 4075594
zbMATH Keywords: algebraic equation
zbMATH Keywords: annihilating analytic functions of operators
author: L. Jódar
reviewed by: Svatoslav Staněk
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90319-9
OpenAlex ID: W2089696659
cites work: Operators which are annihilated by analytic functions and invariant subspaces
cites work: Sous-espaces invariants de type fonctionnel dans les espaces de Banach
cites work: The Drazin Inverse of an Infinite Matrix
cites work: Q3964715
cites work: Q3207128
cites work: Solving Linear Operator Equations
cites work: Q5574200
cites work: ON SOME DIFFERENTIAL-OPERATOR EQUATIONS OF ARBITRARY ORDER
cites work: Q3900188
cites work: Spectral analysis of families of operator polynomials and a generalized Vandermonde matrix II: The infinite dimensional case
cites work: Q3939931
cites work: Q5592564
cites work: Explicit solution of a class of higher-order abstract Cauchy problems
cites work: Q3692314
cites work: On some mathematical principles in the linear theory of damped oscillations of continua II
cites work: Boundary problems for Riccati and Lyapunov equations
cites work: Boundary value problems for second-order differential operator equations
cites work: Boundary-value problems and Cauchy problems for the second-order Euler operator differential equation
cites work: Q3957479
cites work: Q5528211
cites work: Generalized Operator Riccati Equations
cites work: Q5523899
cites work: ON THE COMPLETEn-TUPLE OF ROOTS OF THE OPERATOR EQUATION CORRESPONDING TO A POLYNOMIAL OPERATOR BUNDLE
cites work: Factorization of matrix polynomials with multiple roots
cites work: Q5600360
cites work: Q5645536
cites work: On factorization of operator polynomials and analytic operator functions
cites work: On the operator equation \(BX - XA = Q\)
cites work: Q4726901
description: scientific article; zbMATH DE number 4075594