Geodesic
An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 56-76

Voir la notice de l'article provenant de la source Math-Net.Ru

It is well known how to construct a system of symmetric orthogonal polynomials in an arbitrary finite number of variables from an arbitrary system of orthogonal polynomials on the real line. In the special case of the big $q$-Jacobi polynomials, the number of variables can be made infinite. As a result, in the algebra of symmetric functions, there arises an inhomogeneous basis whose elements are orthogonal with respect to some probability measure. This measure is defined on a certain space of infinite point configurations and hence determines a random point process.
Keywords: Big q-Jacobi polynomials, symmetric functions, Schur functions
Mots-clés : interpolation polynomials, beta distribution. 
@article{FAA_2017_51_3_a3,
     author = {G. I. Olshanskii},
     title = {An analogue of the big $q${-Jacobi} polynomials in the algebra of symmetric functions},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {56--76},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a3/}
}
TY  - JOUR
AU  - G. I. Olshanskii
TI  - An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2017
SP  - 56
EP  - 76
VL  - 51
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a3/
LA  - ru
ID  - FAA_2017_51_3_a3
ER  - 
%0 Journal Article
%A G. I. Olshanskii
%T An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2017
%P 56-76
%V 51
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a3/
%G ru
%F FAA_2017_51_3_a3
G. I. Olshanskii. An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 56-76. http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a3/