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Matrix transformation of univalent power series

Published online by Cambridge University Press:  09 April 2009

F. W. Hartmann  and
T. H. MacGregor
F. W. Hartmann
Affiliation:
Villanova University, U.S.A.
T. H. MacGregor
Affiliation:
State University of New York at Albany, U.S.A.
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Suppose that A = [αnk], (n, k = 0, 1, 2, …), is an indinite matrix with complex entries. A transforms a complex sequence a = {an to a complex sequence {bn = b = Aa where assuming that the series in (1) converges. Each sequence a = {an is uniquely associated with a power series In this way the matrix A transforms a power series into a power series. Specifically, the power series (2) is mapped to the power series where the bn's are given by (1). We are only interested in matrices having the property that each power series analytic in Δ = {z: |z| < 1} maps to a power series analytic in Δ.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 419 - 435
Copyright
Copyright © Australian Mathematical Society 1974

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