On ( j , k ) -symmetrical functions

Piotr Liczberski; Jerzy Połubiński

Mathematica Bohemica (1995)

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

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 ( j , k ) -symmetrical function ( k = 2 , 3 , ⋯ ; j = 0 , 1 , ⋯ , 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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  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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