Algebraic Formalism within the Works of Servois and its Influence on the Development of Linear Operator Theory

2012 ◽  
Author(s):  
Anthony J. Del Latto ◽  
Salvatore J. Petrilli, Jr.
Keyword(s):  
Linear Operator ◽  
Operator Theory ◽  
Algebraic Formalism

Introductory Linear Operator Theory

2002 ◽  
pp. 129-217
Author(s):  
George W. Hanson ◽  
Alexander B. Yakovlev
Keyword(s):  
Linear Operator ◽  
Operator Theory

scholarly journals Some convexity theorems for matrices

1971 ◽  
Vol 12 (2) ◽  
pp. 110-117 ◽  
Author(s):  
P. A. Fillmore ◽  
J. P. Williams
Keyword(s):  
Linear Operator ◽  
Operator Theory ◽  
Bounded Linear Operator ◽  
Numerical Range ◽  
Two Dimensional ◽  
Bounded Linear ◽  
Image Position

The numerical range of a bounded linear operator A on a complex Hilbertspace H is the set W(A) = {(Af, f): ║f║ = 1}. Because it is convex andits closure contains the spectrum of A, the numerical range is often a useful toolin operator theory. However, even when H is two-dimensional, the numerical range of an operator can be large relative to its spectrum, so that knowledge of W(A) generally permits only crude information about A. P. R. Halmos [2] has suggested a refinement of the notion of numerical range by introducing the k-numerical rangesfor k = 1, 2, 3, …. It is clear that W1(A) = W(A). C. A. Berger [2] has shown that Wk(A) is convex.

Linear operator theory of channeled spectropolarimetry

2005 ◽  
Vol 22 (8) ◽  
pp. 1567 ◽  
Author(s):  
Derek S. Sabatke ◽  
Ann M. Locke ◽  
Robert W. McMillan ◽  
Eustace L. Dereniak
Keyword(s):  
Linear Operator ◽  
Operator Theory

scholarly journals Series Solution of a Functional Equation

1965 ◽  
Vol 5 (1) ◽  
pp. 48-55
Author(s):  
W. Pranger
Keyword(s):  
Functional Equation ◽  
Linear Operator ◽  
Operator Theory ◽  
Inversion Formula ◽  
Linear Functional ◽  
Series Solution ◽  
Analytic Solutions ◽  
Linear Functional Equation ◽  
General Operator ◽  
Image Position

In this we will study analytic solutions to the linear functional equation where f and h are given functions, x is a given complex number and the function g is to be found. This is a generalization of Schröder's functional equation. The results obtained are global in nature and the solutions holomorphic. The equation will be viewed from the standpoint of linear operator theory. When studied in this manner one arrives at a general operator inversion formula.

Compensatory tracking performance of children in terms of linear operator theory

1972 ◽  
Vol 36 (5) ◽  
pp. 388-407 ◽  
Author(s):  
N.W.A. Marsh ◽  
J.W.K. Chang ◽  
E. Rose
Keyword(s):  
Linear Operator ◽  
Operator Theory ◽  
Tracking Performance

Real Linear Operator Theory and its Applications

2010 ◽  
Vol 69 (1) ◽  
pp. 113-132 ◽  
Author(s):  
Marko Huhtanen ◽  
Santtu Ruotsalainen
Keyword(s):  
Linear Operator ◽  
Operator Theory ◽  
Real Linear
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