Divided difference operators in equivariant KK-theory

Equivariant KK-theory and noncommutative index theory

The Universal Property of Equivariant Kk-theory

Let G be a locally compact, σ-compact group. We prove that the equivariant KK-theory, KK, is the universal category for functors from G-algebras to abelian groups which are stable, homotopy invariant and split-exact. This is a generalization of Higsons characterisation of (non-equivariant) KK-theory.

Skew Divided Difference Operators and Schubert Polynomials

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with posit...

A divided difference expansion of a divided difference

A divided difference expansion with remainder for a general divided difference is derived that contains Floater’s recent derivative expansion as a special case. key words divided difference, univariate, remainder, interpolation

Computational Divided Differencing and Divided-Difference Arithmetics

Tools for computational differentiation transform a program that computes a numerical function F(x) into a related program that computes F ′(x) (the derivative of F). This paper describes how techniques similar to those used in computational-differentiation tools can be used to implement other program transformations—in particular, a variety of transformations for computational divided differen...