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4 results

  • BESSEL- AND GRÜSS-TYPE INEQUALITIES IN INNER PRODUCT MODULES

  • Senka Banić, Dijana Ilišević, Sanja Varošanec
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 1 / February 2007
    Published online by Cambridge University Press:
    09 February 2007, pp. 23-36
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  • In this paper we give Bessel- and Grüss-type inequalities in an inner product module over a proper $H^*$-algebra or a $C^*$-algebra.

  • Positive Polynomials and Time Dependent Integer-Valued Random Variables

  • B. M. Baker, D. E. Handelman
  • Journal:
    Canadian Journal of Mathematics / Volume 44 / Issue 1 / 01 December 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 3-41
    Print publication:
    01 December 1991
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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.

  • Bounded Solutions of a Functional Inequality

  • Michael Albert, John A. Baker
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 4 / 01 December 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 491-495
    Print publication:
    01 December 1982
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  • It is known that if f is a real valued function on a rational vector space V, δ > 0,

    1

    and if f is unbounded then f(x + y) = f(x)f(y) for all x, y ∊ V. In response to a problem of E. Lukacs, in this paper we study the bounded solutions of (1). For example, it is shown that if f is a bounded solution of (1) then - δ ≤ f(x) ≤ (1 + (1 + 4δ)1/2)/2 for all x ∊ V and these bounds are optimal.