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- W2013842488 abstract "In this paper we study the zero-sets of continuous n-homogeneous polynomials on complex nonseparable Banach spaces. We prove that the zero-set of any complex n-homogeneous polynomial P is a subspace if, and only if, there is a functional ϕ such that P(x)=ϕ (x)n for every x. We give sufficient conditions on the Banach space to ensure that every continuous 2-homogeneous polynomial is identically zero on a nonseparable subspace. Also, we prove that, in the 2-homogeneous case, one of the following three properties holds: P −1(0) is a subspace; P −1(0) is the union of two different subspaces; and P −1(0) is the union of infinitely many different subspaces." @default.
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- W2013842488 date "2008-05-01" @default.
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- W2013842488 title "Zero-sets of complex homogeneous polynomials" @default.
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- W2013842488 doi "https://doi.org/10.1080/03081080600872350" @default.
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