Topics in Hyperplane Arrangements, Polytopes and Box-Splines

1. Auflage. 2010
ISBN: 978-0-387-78962-0
Verlag: Springer

Buch, Englisch, 381 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 684 g

Reihe: Universitext

Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory.

This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.

Zielgruppe

Research

Autoren/Hrsg.

Procesi, Claudio

De Concini, Corrado

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines

Inhaltsverzeichnis

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.