Lecture Notes in Mathematics

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

Authors: Handelman, David E.

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About this book

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.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $29.99
price for USA in USD (gross)
  • ISBN 978-3-540-47951-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA in USD
  • ISBN 978-3-540-18400-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1282
Copyright
1987
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47951-2
DOI
10.1007/BFb0078909
Softcover ISBN
978-3-540-18400-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 138
Topics