Topics in Hyperplane Arrangements, Polytopes and Box-Splines

Paperback | August 30, 2010

byCorrado De Concini, Claudio Procesi

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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.

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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 ...

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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.In its simplest form, the problem is ...

Format:PaperbackDimensions:403 pages, 9.25 × 6.1 × 0.27 inPublished:August 30, 2010Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387789626

ISBN - 13:9780387789620

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Table of Contents

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.

Editorial Reviews

From the reviews:"This book brings together several areas of mathematics that have developed mostly independently over the past 30 years. . the book is self-contained. . provide an illuminating class of examples, which are investigated throughout the book. The writing is consistently clear, with careful attention paid to detail. . the determined reader will find it an ultimately rewarding read, and certainly worth the effort." (Alexander I. Suciu, Mathematical Reviews, Issue 2011 m)"This book revisits the paper of Dahmen and Micchelli and reproves some of their results . by different methods. . The book is written at a relatively elementary level . . A motivated reader will find it well worth the effort." (G. K. Sankaran, Zentralblatt MATH, Vol. 1217, 2011)