Vol. 46(60), pp. 59--70 (1989)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Classes of weighted symmetric functions$^{\ast}$

Tan Cao Tran

Department of Mathematics, Loras College Dubuque, Iowa 52001, USA

Abstract: 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.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition