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Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem (Paperback, 1987 ed.)
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Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem (Paperback, 1987 ed.)
Series: Lecture Notes in Mathematics, 1282
Expected to ship within 10 - 15 working days
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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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