PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 46(60), pp. 5970 (1989) 

Classes of weighted symmetric functions$^{\ast}$Tan Cao TranDepartment of Mathematics, Loras College Dubuque, Iowa 52001, USAAbstract: 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 (MSC2000): 26A99 Full text of the article:
Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.
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