Markov operator in constrained tomography

1992 ◽  
Author(s):  
P. Carrion ◽  
G. Jacovitti ◽  
A. Neri
Keyword(s):  
Markov Operator

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

scholarly journals Stability of the Markov operator and synchronization of Markovian random products

Nonlinearity ◽  
2018 ◽  
Vol 31 (5) ◽  
pp. 1782-1806 ◽  
Author(s):  
Lorenzo J Díaz ◽  
Edgar Matias
Keyword(s):  
Markov Operator ◽  
Random Products

scholarly journals The spectrum of an Adelic Markov operator

2015 ◽  
Vol 64 (5) ◽  
pp. 1465-1512
Author(s):  
Andreas Knauf
Keyword(s):  
Markov Operator

scholarly journals Weak Markov operators

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5453-5457
Author(s):  
Hūlya Duru ◽  
Serkan Ilter
Keyword(s):  
Positive Operator ◽  
Extreme Points ◽  
Markov Operator ◽  
Weak Order ◽  
Markov Operators

Let A and B be f -algebras with unit elements eA and eB respectively. A positive operator T from A to B satisfying T(eA) = eB is called a Markov operator. In this definition we replace unit elements with weak order units and, in this case, call T to be a weak Markov operator. In this paper, we characterize extreme points of the weak Markov operators.

On spectral properties of a family of transfer operators and convergence to stable laws for affine random walks

2008 ◽  
Vol 28 (2) ◽  
pp. 423-446 ◽  
Author(s):  
Y. GUIVARC’H ◽  
EMILE LE PAGE
Keyword(s):  
Random Walk ◽  
Spectral Properties ◽  
Markov Operator ◽  
Dominant Eigenvalue ◽  
Fractional Powers ◽  
Stable Law ◽  
Fourier Operator ◽  
Transfer Operators ◽  
Heisenberg Type ◽  
Normal Law

AbstractWe consider a random walk on the affine group of the real line, we denote by P the corresponding Markov operator on $\mathbb {R}$, and we study the Birkhoff sums associated with its trajectories. We show that, depending on the parameters of the random walk, the normalized Birkhoff sums converge in law to a stable law of exponent α∈ ]0,2[ or to a normal law. The corresponding analysis is based on the spectral properties of two families of associated transfer operators Pt,Tt. The operator Pt is a Fourier operator and is considered here as a perturbation of the Markov operator P=P0 of the random walk. The operator Tt is related to Pt by a symmetry of Heisenberg type and is also considered as a perturbation of the Markov operator T0=T. We prove that these operators have an isolated dominant eigenvalue which has an asymptotic expansion involving fractional powers of t. The parameters of this expansion have simple expressions in terms of tails and moments of the stationary measures of P and T.

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