IJPAM: Volume 84, No. 5 (2013)
FOR MULTIVARIATE POWER SERIES
Turin Polytechnic University in Tashkent
INSPEM, Universiti Putra Malaysia
Abstract. In this paper a new (symmetric) product for matrices, entries of which are located by pair of multi-indices, and norms of such matrices are introduced. They are used to represent multivariate power series as series in one (vector) variable and to introduce a radius of absolute convergence. For the radius of absolute convergence a formula, similar to ordinary Cauchy-Hadamard formula in one variable case, is given. Some open problems related to the radius of absolute convergence are set.
Received: September 5, 2011
AMS Subject Classification: 32A05, 15A60
Key Words and Phrases: multi-index, multivariate power series
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DOI: 10.12732/ijpam.v84i5.2 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395