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The goal of this paper is to describe the $alpha$-cosine transform on functions on a Grassmannian of $i$-planes in an $n$-dimensional real vector space. in analytic terms as explicitly as possible. We show that for all but finitely many complex $alpha$ the $alpha$-cosine transform is a composition of the $(alpha+2)$-cosine transform with an explicitly written (though complicated) O(n)-invariant differential operator. For all exceptional values of $alpha$ except one we interpret the $alpha$-cosine transform explicitly as either the Radon transform or composition of two Radon transforms. Explicit interpretation of the transform corresponding to the last remaining value $alpha$, which is $-(min{i,n-i}+1)$, is still an open problem.
Speech enhancement algorithms based on deep learning have been improved in terms of speech intelligibility and perceptual quality greatly. Many methods focus on enhancing the amplitude spectrum while reconstructing speech using the mixture phase. Sin
This paper continues the study of the lower central series quotients of an associative algebra A, regarded as a Lie algebra, which was started in math/0610410 by Feigin and Shoikhet. Namely, it provides a basis for the second quotient in the case whe
In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Q
We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuils locally analytic socle conjecture for $mathrm{GL}_n(mathbb{Q}_p)$.
Let the vector bundle $mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $mathcal{E}$, also known as the polymology. This is the first par