Geodesic
Classes of Weighted Symmetric Functions
Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 59

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We generalize the concept of the $k$-th symmetric difference in the sense of Stein and Zygmund to that of symmetric difference with respect to a weight system of order $n$ and the concept of symmetrically continuous functions and symmetric functions to that of functions symmetric with respect to a weight system of order $n$. We also study the classes of even symmetry and odd symmetry consisting of functions whose limits to the right and to the left exist at each point; hence, their set of points of discontinuity is countable, and they are in Baire class one. The functions symmetric with respect to a fixed weight system $W_n$ of order $n$ form a linear space $V(W_n)$, and the subclass $B(W_n)$ consisting of bounded functions forms a Banach space with the norm $\|f\|=\sup |f(x)|$.
Classification : 26A99 
@article{PIM_1989_N_S_46_60_a9,
     author = {Tan Cao Tran},
     title = {Classes of {Weighted} {Symmetric} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {59 },
     publisher = {mathdoc},
     volume = {_N_S_46},
     number = {60},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a9/}
}
TY  - JOUR
AU  - Tan Cao Tran
TI  - Classes of Weighted Symmetric Functions
JO  - Publications de l'Institut Mathématique
PY  - 1989
SP  - 59 
VL  - _N_S_46
IS  - 60
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a9/
LA  - en
ID  - PIM_1989_N_S_46_60_a9
ER  - 
%0 Journal Article
%A Tan Cao Tran
%T Classes of Weighted Symmetric Functions
%J Publications de l'Institut Mathématique
%D 1989
%P 59 
%V _N_S_46
%N 60
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a9/
%G en
%F PIM_1989_N_S_46_60_a9
Tan Cao Tran. Classes of Weighted Symmetric Functions. Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 59 . http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a9/