| Title:
|
On $(j,k)$-symmetrical functions (English) |
| Author:
|
Liczberski, Piotr |
| Author:
|
Połubiński, Jerzy |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
13-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$(j,k)$-symmetrical functions |
| Keyword:
|
holomorphic function |
| Keyword:
|
integral formulas |
| Keyword:
|
uniqueness theorem |
| Keyword:
|
mean value of a function |
| Keyword:
|
a variant of Schwarz lemma |
| Keyword:
|
fixed point |
| Keyword:
|
spectrum of an operator |
| MSC:
|
26B40 |
| MSC:
|
26E15 |
| MSC:
|
30A10 |
| MSC:
|
30A99 |
| MSC:
|
32A99 |
| MSC:
|
46G20 |
| idZBL:
|
Zbl 0838.30004 |
| idMR:
|
MR1336943 |
| DOI:
|
10.21136/MB.1995.125897 |
| . |
| Date available:
|
2009-09-24T21:08:30Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125897 |
| . |
| Reference:
|
[1] J. Dieudonne: Grundzüge der modernen Analysis.II Auflage, VEB Deutscher Verlag der Wissenschaften, Berlin, 1972. Zbl 0264.26001, MR 0474358 |
| Reference:
|
[2] W. Fulton J. Harris: Representation theory.Graduate Text Math., Spгinger, 1991. MR 1153249 |
| Reference:
|
[3] E. Janiec: Some uniqueness theorems concerning holomorphic mappings.Demonstratio Math. 23, 4 (1990), 879-892. Zbl 0755.32002, MR 1124740, 10.1515/dema-1990-0407 |
| Reference:
|
[4] R. Mortini: Lösung der Aufgabe 901.El. Math. 39 (1984), 130-131. |
| Reference:
|
[5] J. Mujica: Complex analysis in Banach spaces.Noгth-Holland, Amsterdam, New York, Oxfoгd. Zbl 0586.46040 |
| Reference:
|
[6] A. Pfluger: Varianten des Schwarzschen Lemma.El. Math. 40 (1985), 46-47. Zbl 0566.30021, MR 0803075 |
| Reference:
|
[7] W. Rudin: The fixed-point sets of some holomorphic maps.Bull. Malaysian Math. Soc. (2) 1 (1978), 25-28. Zbl 0413.32012, MR 0506535 |
| Reference:
|
[8] W. Rudin: Real and complex analysis.(second edition). McGraw-Hill Inc, 1974. Zbl 0278.26001, MR 0344043 |
| . |
