Spectral distribution of the free Jacobi process associated with one projection

2014 ◽  
Vol 137 (2) ◽  
pp. 271-296 ◽  
Author(s):  
Nizar Demni ◽  
Taoufik Hmidi
Keyword(s):  
Spectral Distribution ◽  
Jacobi Process

scholarly journals Spectral distribution of the free Jacobi process

2012 ◽  
Vol 61 (3) ◽  
pp. 1351-1368 ◽  
Author(s):  
Nizar Demni ◽  
Tarek Hamdi ◽  
Taoufik Hmidi
Keyword(s):  
Spectral Distribution ◽  
Jacobi Process

Inverse of the flow and moments of the free Jacobi process associated with one projection

2018 ◽  
Vol 07 (02) ◽  
pp. 1850001 ◽  
Author(s):  
Nizar Demni ◽  
Tarek Hamdi
Keyword(s):  
General Theory ◽  
Spectral Distribution ◽  
Unitary Operator ◽  
Boundary Behavior ◽  
Open Unit ◽  
Open Unit Disc ◽  
Absolutely Continuous ◽  
Herglotz Function ◽  
Jacobi Process ◽  
Löwner Equation

This paper is a companion to a series of papers devoted to the study of the spectral distribution of the free Jacobi process associated with a single projection. Actually, we note that the flow derived in [N. Demni and T. Hmidi, Spectral distribution of the free Jacobi process associated with one projection, Colloq. Math. 137(2) (2014) 271–296] solves a radial Löwner equation and as such, the general theory of Löwner equations implies that it is univalent in some connected region in the open unit disc. We also prove that its inverse defines the Aleksandrov–Clark measure at [Formula: see text] of some Herglotz function which is absolutely-continuous with an essentially bounded density. As a by-product, we deduce that [Formula: see text] does not belong to the continuous singular spectrum of the unitary operator whose spectral dynamics are governed by the flow. Moreover, we use a previous result due to the first author in order to derive an explicit, yet complicated, expression of the moments of both the unitary and the free Jacobi processes. The paper is closed with some remarks on the boundary behavior of the flow’s inverse.

Spectral distribution of a thin window rhodium target x-ray spectrographic tube

1971 ◽  
Vol 43 (7) ◽  
pp. 934-936 ◽  
Author(s):  
J. V. Gilfrich ◽  
P. G. Burkhalter ◽  
R. R. Whitlock ◽  
E. S. Warden ◽  
L. S. Birks
Keyword(s):  
Spectral Distribution ◽  
X Ray
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