On Hörmander’s ratio theorems

Jamjoom, Fatma B.; Zaheer, N.

doi:10.1090/S0002-9939-1988-0920992-6

On Hörmander’s ratio theorems
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Proc. Amer. Math. Soc. 102 (1988), 311-316 Request permission

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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