YANG LIU'S MATH BLOG

On the Range of Cosine Transform of Distributions for Torus-invariant Complex Minkowski Spaces

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In this paper, we study the ranges of (absolute value) cosine trans- forms for which we give a proof for an extended surjectivity t heorem by mak- ing applications of the Fredholm’s theorem in integral equa tions, and show a Hermitian characterization theorem for complex Minkowsk i metrics on C^n . Moreover, we parametrize the Grassmannian in an elementary linear algebra approach, and give a characterization on the image of the (ab solute value) co- sine transform on the space of distributions on the Grassman nian Gr_2 ( C^ 2 ), by computing the coefficients in the Legendre series expansion o f distributions.

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