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

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.