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- catalog abstract "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.".
- catalog contributor b1874339.
- catalog created "1987.".
- catalog date "1987".
- catalog date "1987.".
- catalog dateCopyrighted "1987.".
- catalog description "Bibliography: p. 129-130.".
- catalog 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.".
- catalog extent "x, 136 p. ;".
- catalog hasFormat "Positive polynomials, convex integral polytopes, and a random walk problem.".
- catalog identifier "0387184007 (U.S.)".
- catalog identifier "3540184007 (Berlin)".
- catalog isFormatOf "Positive polynomials, convex integral polytopes, and a random walk problem.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1282.".
- catalog isPartOf "Lecture notes in mathematics ; 1282".
- catalog issued "1987".
- catalog issued "1987.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Positive polynomials, convex integral polytopes, and a random walk problem.".
- catalog subject "Algebra.".
- catalog subject "C*-algebras.".
- catalog subject "Geometry.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Mathematics.".
- catalog subject "Polynomials.".
- catalog subject "Polytopes.".
- catalog subject "QA3 .L28 no. 1282 QA326".
- catalog subject "Random walks (Mathematics)".
- catalog title "Positive polynomials, convex integral polytopes, and a random walk problem / David E. Handelman.".
- catalog type "text".