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

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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/}
}
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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/