Factorization of matrix functions and their inverses via power product expansions

被引：4
作者：
Gingold, H. [1 ]
机构：
[1] W Virginia Univ, Dept Math, Morgantown, WV 26505 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 11-12期
关键词：
Power products; Inverse power products; Power series; Non-commutative; Matrix functions; Expansions; Convergence; ANALYTIC-FUNCTIONS; INFINITE PRODUCTS;
D O I：
10.1016/j.laa.2008.12.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The conversion of a power series with matrix coefficients into an infinite product of certain elementary matrix factors is studied. The expansion of a power series with matrix coefficients as the inverse of an infinite product of elementary factors is also analyzed. Each elementary factor is the sum of the identity matrix and a certain matrix coefficient multiplied by a certain power of the variable. The two expansions provide us with representations of a matrix function and its inverse by infinite products of elementary factors. Estimates on the domain of convergence of the infinite products are given. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：2835 / 2858
页数：24
相关论文
共 24 条
  • [1] Andrews GE., 1976, THEORY PARTITIONS
  • [2] Birkhoff G., 1965, A Survey of Modern Algebra, Vthird
  • [3] Borofsky S., 1931, ANN MATH, V32, P23, DOI [10.2307/1968411, DOI 10.2307/1968411]
  • [4] Borofsky S., 1930, TOHOKU MATH J, V34, P263
  • [5] Feld J.M., 1930, B AM MATH SOC, V36, P284, DOI DOI 10.1090/S0002-9904-1930-04936-8
  • [6] The expansion of analytic functions in generalized Lambert series.
    Feld, JM
    [J]. ANNALS OF MATHEMATICS, 1932, 33 : 139 - 142
  • [7] GINGOLD H, 1988, UTILITAS MATHEMATICA, V34, P143
  • [8] GINGOLD H, 1990, UTILITAS MATHEMATICA, V37, P79
  • [9] Analytic properties of power product expansions
    Gingold, H
    Knopfmacher, A
    [J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1995, 47 (06): : 1219 - 1239
  • [10] Gingold H., 1993, ANALYSIS, V13, P133
123