ENGLISH

Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem

By David E. Handelman (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1987
ISBN
9780387184005, 0-387-18400-7
DOI
10.1007/BFb0078909
LCC
QA3 .L28 no. 1282,QA326 .L28 no. 1282
Open Library ID
OL2086172M
Language
english
Format
DJVU
Filesize
1007 kB (1031672 bytes)
Series
Lecture Notes in Mathematics 1282
Edition
1
Pages
138\152
Library
mexmat
Time added
2009-07-20 03:45:11
Analysis; Algebra; Geometry

Description

Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as well as specialists in the areas mentioned.

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