A new positive linear functional filters design for positive linear systems

2014 ◽  
Author(s):  
M. Ezzine ◽  
M. Darouach ◽  
H. Souley Ali ◽  
H. Messaoud
Keyword(s):  
Linear Systems ◽  
Linear Functional ◽  
Positive Linear Functional

A Lebesgue Decomposition Theorem for C* Algebras

1972 ◽  
Vol 15 (1) ◽  
pp. 87-91 ◽  
Author(s):  
Michael Henle
Keyword(s):  
Absolute Continuity ◽  
Linear Functional ◽  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
C Algebras ◽  
Positive Linear Functional ◽  
Decomposition Theorems

This paper, by generalizing von Neumann's proof of the Radon-Nikodym and Lebesgue decomposition theorems [3], obtains analogous results for positive linear functional on a C* algebra. The concept of "absolute continuity" used and the Radon-Nikodym portion of the resulting theorem are due to Dye [2].

Integration Theory

2021 ◽  
pp. 341-444
Author(s):  
Adel N. Boules
Keyword(s):  
Linear Functional ◽  
Integration Theory ◽  
General Measure ◽  
Radon Measures ◽  
Lp Spaces ◽  
Approximation Theorems ◽  
Positive Linear Functional ◽  
Product Measures ◽  
Compactly Supported Functions ◽  
Nikodym Theorem

The Lebesgue measure on ?n (presented in section 8.4) is a pivotal component of this chapter. The approach in the chapter is to extend the positive linear functional provided by the Riemann integral on the space of continuous, compactly supported functions on ?n (presented in section 8.1). An excursion on Radon measures is included at the end of section 8.4. The rest of the sections are largely independent of sections 8.1 and 8.4 and constitute a deep introduction to general measure and integration theories. Topics include measurable spaces and measurable functions, Carathéodory’s theorem, abstract integration and convergence theorems, complex measures and the Radon-Nikodym theorem, Lp spaces, product measures and Fubini’s theorem, and a good collection of approximation theorems. The closing section of the book provides a glimpse of Fourier analysis and gives a nice conclusion to the discussion of Fourier series and orthogonal polynomials started in section 4.10.

Sign in / Sign up

Export Citation Format

Share Document