Unitary Systems and Characteristic Operator Functions

1993 ◽  
pp. 700-786
Author(s):  
I. Gohberg ◽  
M. A. Kaashoek ◽  
S. Goldberg
Keyword(s):  
Characteristic Operator ◽  
Operator Functions

About the general solution of a linear homogeneous differential equation in a Banach space in the case of complex characteristic operators

2019 ◽  
pp. 211-217 ◽  
Author(s):  
Vasiliy. I Fomin
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
General Solution ◽  
Operator Equation ◽  
Bounded Operator ◽  
Characteristic Operator ◽  
Homogeneous Differential Equation ◽  
Operator Functions ◽  
Linear Homogeneous Differential Equation ◽  
Real Argument

A linear inhomogeneous differential equation (LIDE) of the n th order with constant bounded operator coefficients is studied in Banach space. Finding a general solution of LIDE is reduced to the construction of a general solution to the corresponding linear homogeneous differential equation (LHDE). Characteristic operator equation for LHDE is considered in the Banach algebra of complex operators. In the general case, when both real and complex operator roots are among the roots of the characteristic operator equation, the n -parametric family of solutions to LHDE is indicated. Operator functions eAt ; sinBt ; cosBt of real argument t ∈ [0;∞) are used when building this family. The conditions under which this family of solutions form a general solution to LHDE are clarified. In the case when the characteristic operator equation has simple real operator roots and simple pure imaginary operator roots, a specific form of such conditions is indicated. In particular, these roots must commute with LHDE operator coefficients. In addition, they must commute with each other. In proving the corresponding assertion, the Cramer operator-vector rule for solving systems of linear vector equations in a Banach space is applied

Linearization of operator functions on arbitrary open sets

1978 ◽  
Vol 1 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Bert den Boer
Keyword(s):  
Operator Functions

On the trace of certain rational operator functions

1992 ◽  
Vol 15 (1) ◽  
pp. 30-42 ◽  
Author(s):  
Hansj�rg Linden ◽  
Josef Menzel
Keyword(s):  
Operator Functions

Differentiation of Operator Functions and Perturbation Bounds

1998 ◽  
Vol 191 (3) ◽  
pp. 603-611 ◽  
Author(s):  
Rajendra Bhatia ◽  
Dinesh Singh ◽  
Kalyan B. Sinha
Keyword(s):  
Perturbation Bounds ◽  
Operator Functions
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