MATHEMATICA BOHEMICA, Vol. 120, No. 1, pp. 13-28, 1995

On $(j,k)$-symmetrical functions

Piotr Liczberski, Jerzy Polubinski

Institute of Mathematics, Technical University of Lodz, ul. Zwirki 36, 90-924 Lodz, Poland

Abstract: In the present paper the authors study some families of functions from a complex linear space $X$ into a complex linear space $Y$. They introduce the notion of $(j,k)$-symmetrical function ($k=2,3,\dots$; $j=0,1,\dots,k-1$) which is a generalization of the notions of even, odd and $k$-symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset $U$ of $X$ can be uniquely represented as the sum of an even function and an odd function.

Keywords: $(j,k)$-symmetrical functions, holomorphic function, integral formulas, uniqueness theorem, mean value of a function, a variant of Schwarz lemma, fixed point, spectrum of an operator.

Classification (MSC91): 30A, 32A, 32M, 46A

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