Vol. 29, No. 3, 1969

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Maximum term of a power series in one and several complex variables

J. Gopala Krishna

Vol. 29 (1969), No. 3, 609–622

In this paper we discuss results leading to a description of an algebraic structure constituted by power series with the same maximum term in several complex variables, and use the description to estimate the maximum modulus of any of the series in terms of its maximum term and its central index, and obtain some useful asymptotic relations. We observe that certain crucial Valiron-type theorems, in the case of several variables, are by no easy or routine means reached through Valiron-type techniques.

Mathematical Subject Classification
Primary: 32.10
Secondary: 30.00
Received: 19 March 1968
Published: 1 June 1969
J. Gopala Krishna