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On composite polynomials whose zeros are in a half-plane

Published online by Cambridge University Press:  17 April 2009

Abdul Aziz
Abdul Aziz
Affiliation:
Post–Graduate Department of Mathematics, University of Kashmir, Hazratbal Srinagar – 190006, Kashmir, INDIA.
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Let P(z) and Q(z) be two polynomials of the same degree n. If P(z) and Q(z) are apolar and if one of then has all its zeros in a circular region C, then according to a famous result known as Grace's Apolarity Theorem, the other will have at least one zero in C. In this paper we relax the condition that P(z) and Q(z) are of the same degree and present some generalizations of Grace's Apolarity theorem for the case when the circular region C is a closed half-plane. As an application of these results, we also generalize some results of Walsh and Szegö.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 449 - 460
Copyright
Copyright © Australian Mathematical Society 1987

References

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