We consider a sequence, of random length M, of independent, continuous observations Xi, 1 ≤ i ≤ M, where M is geometric, X1 has cumulative distribution function (CDF) G, and Xi, i ≥ 2, have CDF F. Let N be the number of upper records and let Rn, n ≥ 1, be the nth record value. We show that N is independent of F if and only if G(x) = G0(F(x)) for some CDF G0, and that if E(|X2|) is finite then so is E(|Rn|), n ≥ 2, whenever N ≥ n or N = n. We prove that the distribution of N, along with appropriately chosen subsequences of E(Rn), characterize F and G and, along with subsequences of E(Rn - Rn-1), characterize F and G up to a common location shift. We discuss some applications to the identification of the wage offer distribution in job search models.

We consider a random record model from a continuous parent X with cumulative distribution function F, where the number of available observations is geometrically distributed. We show that, if E(|X|) is finite, then so is E(|Rn|) whenever Rn, the nth upper record value, exists. We prove that appropriately chosen subsequences of E(Rn) characterize F and subsequences of E(Rn − Rn−1) identify F up to a location shift. We discuss some applications to the identification of wage-offer distributions in job search models.

We establish two characterizations of local Laplace transforms in Banach spaces. The first result follows the classic approach of Widder, while the second is in terms of vector-valued moment sequences. As a consequence, we derive characterizations of nilpotent semigroups.

AMS 2000 Mathematics subject classification: Primary 44A10; 47D03

Hilbert spaces of analytic functions generated by rotationally symmetric measures on disks and annuli are studied. A domination relation between function norm and weighted sums of integral means on circles is developed. The function norm and the weighted sum take the same value for a specified class of polynomials. This class can be varied according to two parameters. Parts of the construction carry over to other Banach spaces of analytic of harmonic functions. Counterexamples illuminating properties of the complex method of interpolation appear as a byproduct.