【摘 要】
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The space of convex rational cones is equipped with a connected coalgebra structure,which is further generalized to decorated cones by means of a differenti
【出 处】
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2014 Workshop on Algebraic Geometry(2014代数几何研讨会)
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The space of convex rational cones is equipped with a connected coalgebra structure,which is further generalized to decorated cones by means of a differentiation procedure.Regularized discrete sums on integer points on convex rational cones lie in a class of germs of meromorphic functions which allows for a linear complement to the algebra of holomorphic functions.The Algebraic Birkhoff Factorization of Connes and Kreimer adapted to this context gives rise to a convolution factorization of discrete sums on integer points on cones.This factorization is shown to coincide with the classical Euler-Maclaurin formula generalized to rational convex cones by Berline and Vergne by means of an interpolating holomorphic function.
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