# On $\left(j,k\right)$-symmetrical functions

Mathematica Bohemica (1995)

• Volume: 120, Issue: 1, page 13-28
• ISSN: 0862-7959

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## Abstract

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n 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 $\left(j,k\right)$-symmetrical function ($k=2,3,\cdots$; $j=0,1,\cdots ,k-1$) 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.

## How to cite

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Liczberski, Piotr, and Połubiński, Jerzy. "On $(j,k)$-symmetrical functions." Mathematica Bohemica 120.1 (1995): 13-28. <http://eudml.org/doc/247789>.

@article{Liczberski1995,
abstract = {n 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.},
author = {Liczberski, Piotr, Połubiński, Jerzy},
journal = {Mathematica Bohemica},
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},
language = {eng},
number = {1},
pages = {13-28},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $(j,k)$-symmetrical functions},
url = {http://eudml.org/doc/247789},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Liczberski, Piotr
AU - Połubiński, Jerzy
TI - On $(j,k)$-symmetrical functions
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 1
SP - 13
EP - 28
AB - n 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.
LA - eng
KW - $(j,k)$-symmetrical functions; holomorphic function; integral formulas; uniqueness theorem; mean value of a function; a variant of Schwarz lemma; fixed point; spectrum of an operator
UR - http://eudml.org/doc/247789
ER -

## References

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1. J. Dieudonne, Grundzüge der modernen Analysis, II Auflage, VEB Deutscher Verlag der Wissenschaften, Berlin, 1972. (1972) Zbl0264.26001MR0474358
2. W. Fulton J. Harris, Representation theory, Graduate Text Math., Spгinger, 1991. (1991) MR1153249
3. E. Janiec, 10.1515/dema-1990-0407, Demonstratio Math. 23, 4 (1990), 879-892. (1990) Zbl0755.32002MR1124740DOI10.1515/dema-1990-0407
4. R. Mortini, Lösung der Aufgabe 901, El. Math. 39 (1984), 130-131. (1984)
5. J. Mujica, Complex analysis in Banach spaces, Noгth-Holland, Amsterdam, New York, Oxfoгd. Zbl0586.46040
6. A. Pfluger, Varianten des Schwarzschen Lemma, El. Math. 40 (1985), 46-47. (1985) Zbl0566.30021MR0803075
7. W. Rudin, The fixed-point sets of some holomorphic maps, Bull. Malaysian Math. Soc. (2) 1 (1978), 25-28. (1978) Zbl0413.32012MR0506535
8. W. Rudin, Real and complex analysis, (second edition). McGraw-Hill Inc, 1974. (1974) Zbl0278.26001MR0344043

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