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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On Hörmander's ratio theorems


Authors: Fatma B. Jamjoom and N. Zaheer
Journal: Proc. Amer. Math. Soc. 102 (1988), 311-316
MSC: Primary 30C15,; Secondary 12D10
DOI: https://doi.org/10.1090/S0002-9939-1988-0920992-6
MathSciNet review: 920992
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Abstract: In this paper we prove a theorem concerning the coincidence of ranges of the ratio of abstract homogeneous polynomials and the corresponding ratio of their polars. We employ the coincidence theorem on symmetric multilinear forms (proved recently by the authors [6 or 5]) to prove our theorem. The main result deduces two ratio theorems due to Hörmander [4], one being an improvement upon his version in the complex plane.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0920992-6
Keywords: Abstract homogeneous polynomials and their polars, symmetric multilinear forms, generalized circular regions, circular cones, hermitian cones
Article copyright: © Copyright 1988 American Mathematical Society