Positive Polynomials and Time Dependent Integer-Valued Random Variables
Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 3-41

Voir la notice de l'article provenant de la source Cambridge University Press

Let {Pi } be a sequence of real (Laurent) polynomials each of which has no negative coefficients, and suppose that f is a real polynomial. Consider the problem of deciding whetherfor all integers k, there exists Nsuch that the product of polynomials(*) Pk+1. Pk+2.....Pk+N ·ƒ has no negative coefficients.
DOI : 10.4153/CJM-1992-001-6
Mots-clés : 60F15, 19K14, 46L80, 46A55, 26D99, 46A40, 60F20, 52A07, 60J15, 60J50, 62E20
Baker, B. M.; Handelman, D. E. Positive Polynomials and Time Dependent Integer-Valued Random Variables. Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 3-41. doi: 10.4153/CJM-1992-001-6
@article{10_4153_CJM_1992_001_6,
     author = {Baker, B. M. and Handelman, D. E.},
     title = {Positive {Polynomials} and {Time} {Dependent} {Integer-Valued} {Random} {Variables}},
     journal = {Canadian journal of mathematics},
     pages = {3--41},
     year = {1991},
     volume = {44},
     number = {1},
     doi = {10.4153/CJM-1992-001-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-001-6/}
}
TY  - JOUR
AU  - Baker, B. M.
AU  - Handelman, D. E.
TI  - Positive Polynomials and Time Dependent Integer-Valued Random Variables
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 3
EP  - 41
VL  - 44
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-001-6/
DO  - 10.4153/CJM-1992-001-6
ID  - 10_4153_CJM_1992_001_6
ER  - 
%0 Journal Article
%A Baker, B. M.
%A Handelman, D. E.
%T Positive Polynomials and Time Dependent Integer-Valued Random Variables
%J Canadian journal of mathematics
%D 1991
%P 3-41
%V 44
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-001-6/
%R 10.4153/CJM-1992-001-6
%F 10_4153_CJM_1992_001_6

[A] Alfsen, E., Compact convex sets and boundary integrals. Ergebnisse d. Math., Springer-Verlag, Berlin, 1971. Google Scholar

[AE] Asimow, L. and Ellis, A.J., Convexity theory and its applications in functional analysis. Academic Press, 1980. Google Scholar

[Ef] Effros, E.G., Dimensions and C*-algebras. CBMS 46, Amer. Math. Soc, 1984. Google Scholar

[EHS] Effros, E.G., Handelman, D.E. and Shen, C.-L., Dimension groups and their affine representations, Amer. J. Math. 102(1980), 385–407. Google Scholar

[El] Elliott, G.A., On the classification of inductive limits of sequences of semisimple finite dimensional algebras, J. Algebra 38(1976), 29–44. Google Scholar

[G] Goodearl, K.R., Partially ordered abelian groups with interpolation. Mathematical Surveys and Monographs 20, Amer. Math. Soc, 1986. Google Scholar

[GH] Goodearl, K. R. and Handelman, D.E., Metric completions of partially ordered abelian groups, Indiana U. Math. J. 29(1980), 861–895. Google Scholar

[GH1] Goodearl, K. R., Rank functions and KQ of regular rings, J. of Pure and Applied Algebra 7(1976), 195–216. Google Scholar

[GHL] Goodearl, K.R., Handelman, D.E. and Lawrence, J.W., Affine representations of Grothendieck groups and applications to Rickart C* -Algebras and N0-continuous regular rings. Memoirs of the A.M.S. 234(1980), 163 p. + vii. Google Scholar

[HI] Handelman, D.E., Positive polynomials and product type actions of compact groups. Memoirs of the A.M.S. 320(1985), 79 p.+ xi. Google Scholar

[H2] Handelman, D.E., Deciding eventual positivity of polynomials, Ergodic Theory and Dynamical Systems 6(1985), 57–79. Google Scholar

[H3] Handelman, D.E., Positive polynomials, convex integral poly topes, and a random walk problem. Springer-Verlag Lecture Notes in Mathematics 1282, 1987. 142 p. Google Scholar

[HR1] Handelman, D.E. and Rossmann, W., Product type actions of finite and compact groups, Indiana U. Math. J. 33(1984), 479–509. Google Scholar

[HR2] , Actions of compact groups on AF C*-algebras, Illinois J. Math. 29(1985), 51–95. Google Scholar

[HLP] Hardy, G.H., Littlewood, J.E. and Pôlya, G., Inequalities. Cambridge University Press, 1951. Google Scholar

[lb] Ibragimov, I.A., On the composition of unimodal distributions, Theory of Probability and its Applications 1(1956)255–260. Google Scholar

[K] Kerov, S.V., Combinatorial examples in the theory of AF algebras (in Russian), Akad. Nauk. Zap. Notes of the Scientific Seminar LOMI 172(1989), 55–67. Google Scholar

[McD] McDonald, D. R., On local limit theorems for integer-valued random variables, Theory of Probability and Statistics Akad. Nauk. 3(1979), 607–614. Google Scholar

[Me] Meissner, E., Uber positive Darstellung von Polynomen, Math. Ann. 70(1911), 223–235. Google Scholar

[Mi] Mineka, J., A criterion for tail events for sums of independent random variables, Z. Wahrscheinlichkeitstheorie verw. Geb. 25(1973), 163–170. Google Scholar

Cité par Sources :