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
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/
@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 },
year = {1989},
volume = {_N_S_46},
number = {60},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a9/}
}