Lagrange multipliers for functions of infinitely many variables
Lagrange multipliers for functions of infinitely many variables
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DOI：
10.1090/s0002-9904-1934-05840-3
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发表时间：
1934-04
影响因子：
1.3
通讯作者：
L. W. Cohen
中科院分区：
文献类型：
--
作者：
L. W. Cohen
本文的目的是将拉格朗日乘子定理推广到无穷多个变量的函数在无穷多个辅助条件下的最大值的情形。潜在的隐函数定理使用是由于哈特。f证明采用了两个引理正常的决定因素和相关的线性方程组似乎已被忽视。J其中一个偶然呈现一个假设在哈特的隐函数定理多余的。
The purpose of this note is to extend the Lagrange multiplier theorem to the case of a maximum of a function of infinitely many variables subject to an infinity of auxiliary conditions. The underlying implicit function theorems used are due to Hart.f The proof employs two lemmas on normal determinants and associated linear systems of equations which seem to have been overlooked. J One of these incidentally renders one assumption in Hart 's implicit function theorem redundant.