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Positive Polynomials and Time Dependent Integer-Valued Random Variables

Published online by Cambridge University Press:  20 November 2018

B. M. Baker  and
D. E. Handelman
B. M. Baker
Affiliation:
Mathematics Department, U. S. Naval Academy, Annapolis, Maryland USA 21402, g04195%n [email protected]
D. E. Handelman
Affiliation:
Mathematics Department, University of Ottawa, Ottawa, Ontario KIN 6N5, dehsg%[email protected]
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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 whether

for all integers k, there exists Nsuch that the product of polynomials

(*) Pk+1. Pk+2.....Pk+N·ƒ has no negative coefficients.

Keywords

60F1519K1446L8046A5526D9946A4060F2052A0760J1560J5062E20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 3 - 41
Copyright
Copyright © Canadian Mathematical Society 1991

References

[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