Topics in hyperplane arrangements, polytopes and box-splines

Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of mathematics 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. The discussion is divided into five extensive parts; the first of which provides basic material on convex sets, combinatorics, polytopes, Laplace and Fourier transforms, and the language of modules over the Weyl algebra. The following four sections focus on the differentiable case, discrete case, and several applications, e.i., two independent chapters explore the conputations of De Rham cohomology for the complement of a hyperplane or toric arrangement. This book, written by two distinguished authors, engages a broad audience by providing a strong foudation in very important areas. This bookmay be used in a classroom setting as well as a reference for researchers. Combines various branches of mathematics including combinatorics, differential and difference equations, approximation theory, and module theory Solves the algebraic problems by module theory under the algebra of differential or difference operators Interprets the results inverting Laplace transform directly Provides new approaches to fundamental techniques and methods INDICE: Introduction.- I Preliminaries. 1 Polytopes. 2 Hyperplane Arrangements. 3 Fourier and Laplace Transforms. 4 Modules Over the Weyl Algebra. 5 Differential and Difference Equations. 6 Approximation Theory I.- II The Differentiable Case. 7 Splines. 8 Rx as a D-Module. 9 The function Tx. 10 Cohomology. 11 Differential Equations.- III The Discrete Case. 12 Partition Functions. 13 Toric Arrangements. 14 Cohomology of Toric Arrangements. 15 Difference Equations. 16 Applications. 17 Approximation Theory II.- IV The Wonderful Model. 18 Minimal Models.

• ISBN: 978-0-387-78962-0
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 395
• Fecha Publicación: 01/10/2008
• Nº Volúmenes: 1
• Idioma: Inglés