Covariance-Stationary Vector Processes

2020 ◽  
pp. 257-290
Keyword(s):  
Stationary Vector

scholarly journals Translatable radii of an operator in the direction of another operator II

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Kallol Paul
Keyword(s):  
Eigenvalue Problem ◽  
Unit Vector ◽  
Generalized Eigenvalue Problem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Eigenvalue ◽  
Necessary And Sufficient ◽  
Stationary Vector

AbstractOne of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work [PAUL, K.: Translatable radii of an operator in the direction of another operator, Scientae Mathematicae 2 (1999), 119–122] is studied in details. A necessary and sufficient condition for a unit vector f to be a stationary vector of the generalized eigenvalue problem Tf = λAf is obtained. Finally a theorem of Williams ([WILLIAMS, J. P.: Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129–136]) is generalized to obtain a translatable radius of an operator in the direction of another operator.

scholarly journals Green's functions for polarized radiative transfer equation in different geometries

2011 ◽  
Vol 7 (S283) ◽  
pp. 358-359
Author(s):  
Juris Freimanis
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Green's Functions ◽  
Radiative Transfer Equation ◽  
Green’S Functions ◽  
Analytic Solutions ◽  
Cylindrical Symmetry ◽  
Exact Analytic Solutions ◽  
Spherical And Cylindrical Symmetry ◽  
Stationary Vector

AbstractA review of some earlier exact analytic solutions of monochromatic stationary vector radiative transfer equation in homogeneous infinite medium is given. It is stressed that Green's functions for plane-parallel, spherical and cylindrical symmetry are expressed through derivatives and integrals from basically one and the same set of functions.

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