A Radon-nikodym-theorem for operators with an application to spectral theory

2008 ◽  
pp. 345-355 ◽  
Author(s):  
M. Wolff
Keyword(s):  
Spectral Theory ◽  
Nikodym Theorem

Separation and Approximation in Topological Vector Lattices

1959 ◽  
Vol 11 ◽  
pp. 286-296 ◽  
Author(s):  
Solomon Leader
Keyword(s):  
Spectral Theory ◽  
Vector Lattice ◽  
Weierstrass Theorem ◽  
Fundamental Lemma ◽  
Vector Lattices ◽  
Integrable Functions ◽  
Nikodym Theorem

Spectral theory in its lattice-theoretic setting proves abstractly that the indicators of measurable sets generate the space L of Lebesgue-integrable functions on an interval. We are concerned here with abstractions suggested by the fact that indicators of intervals suffice to generate L. Our results show that the approximation of arbitrary elements of a topological vector lattice rests upon the ability to separate disjoint elements/ and g by an operation that behaves in the limit like a projection annihilating/ and leaving g invariant.The introduction of this concept of separation together with the notion of limit unit leads (via the Fundamental Lemma) to abstract generalizations of the Radon-Nikodym Theorem (Theorem 1) and the Stone-Weierstrass Theorem (Theorem 3).

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

SPECTRAL THEORY OF 2-D PHOTONIC CRYSTALS: ANALYTICAL GROUNDS

2016 ◽  
Vol 75 (16) ◽  
pp. 1417-1433 ◽  
Author(s):  
Yurii Konstantinovich Sirenko ◽  
K. Yu. Sirenko ◽  
H. O. Sliusarenko ◽  
N. P. Yashina
Keyword(s):  
Photonic Crystals ◽  
Spectral Theory

Spectral Theory for Skip-Free Markov Chains

1989 ◽  
Vol 3 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Joseph Abate ◽  
Ward Whitt
Keyword(s):  
Markov Chains ◽  
Spectral Theory ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage Times ◽  
Simple Relationship ◽  
First Passage ◽  
Birth And Death Processes ◽  
The Laplace Transform ◽  
Passage Times

The distribution of upward first passage times in skip-free Markov chains can be expressed solely in terms of the eigenvalues in the spectral representation, without performing a separate calculation to determine the eigenvectors. We provide insight into this result and skip-free Markov chains more generally by showing that part of the spectral theory developed for birth-and-death processes extends to skip-free chains. We show that the eigenvalues and eigenvectors of skip-free chains can be characterized in terms of recursively defined polynomials. Moreover, the Laplace transform of the upward first passage time from 0 to n is the reciprocal of the nth polynomial. This simple relationship holds because the Laplace transforms of the first passage times satisfy the same recursion as the polynomials except for a normalization.

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