Topics in Hyperplane Arrangements, Polytopes and Box-Splines

• Main Authors: De Concini, Corrado (Author), Procesi, Claudio (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Edition: 1.
• Series: Universitext
• Subjects: Mathematics.; Algebra.; Matrix theory.; Mathematical analysis.; Analysis (Mathematics).; Approximation theory.; Differential equations.; Geometry.; Analysis.; Linear and Multilinear Algebras, Matrix Theory.; Ordinary Differential Equations.; Approximations and Expansions.

Several mathematical areas that have been developed independently over the last 30 years are brought together revolving around the computation of the number of integral points in suitable families of polytopes. The problem is formulated here in terms of partition functions and multivariate splines....

Table of Contents:

• Preliminaries
• Polytopes
• Hyperplane Arrangements
• Fourier and Laplace Transforms
• Modules over the Weyl Algebra
• Differential and Difference Equations
• Approximation Theory I
• The Di?erentiable Case
• Splines
• RX as a D-Module
• The Function TX
• Cohomology
• Differential Equations
• The Discrete Case
• Integral Points in Polytopes
• The Partition Functions
• Toric Arrangements
• Cohomology of Toric Arrangements
• Polar Parts
• Approximation Theory
• Convolution by B(X)
• Approximation by Splines
• Stationary Subdivisions
• The Wonderful Model
• Minimal Models.