Functional equations and Weierstrass sigma-functions

被引：8
|
作者：
Illarionov, A. A. [1 ]
机构：
[1] Russian Acad Sci, Inst Appl Math, Khabarovsk Div, Far Eastern Branch, Khabarovsk, Russia
来源：
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2016年 / 50卷 / 04期
基金：
俄罗斯科学基金会;
关键词：
functional equation; Weierstrass sigma-function; elliptic function; addition theorem; trilinear functional equation;
D O I：
10.1007/s10688-016-0159-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is proved that if an entire function f: a", -> a", satisfies an equation of the form alpha (1)(x)beta (1)(y) + alpha (2)(x)beta (2)(y) + alpha (3)(x)beta (3)(y), x,y a C, for some alpha (j) , beta (j) : a", -> a", and there exist no and Ee for which , then f(z) = exp(Az (2) + Bz + C) a (TM) sigma (I")(z - z (1)) a (TM) sigma (I")(z - z (2)), where I" is a lattice in a",; sigma (I") is the Weierstrass sigma-function associated with I"; A,B,C, z (1), z (2) a a",; and .
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页码：281 / 290
页数：10
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