Bounds on Order of Indeterminate Moment Sequences

On the order of indeterminate moment problems

For an indeterminate moment problem we denote the orthonormal polynomials by Pn. We study the relation between the growth of the function P (z) = ( ∑∞ n=0 |Pn(z)|) and summability properties of the sequence (Pn(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zPn(z) = bnPn+1(z) + anPn(z) + bn−1Pn−1(z), we show that the function P is of order ...

Logarithmic order and type of indeterminate moment problems II

This paper deals with the indeterminate moment problem on the real line. We are given a positive measure μ on R having moments of all orders and we assume that μ is not determined by its moments. For details about the indeterminate moment problem see the monographs by Akhiezer, by Shohat and Tamarkin or the survey paper by Berg. Our notation follows that of Akhiezer. In this indeterminate situa...

On in nitely divisible solutions to indeterminate moment problems

Bounds on Universal Sequences

Universal sequences for graphs, a concept introduced by Aleliunas [M. are studied. By letting U(d, n) denote the minimum length of a universal sequence for d-regular undirected graphs with n nodes, the latter paper has proved the upper bound U(d, n)= O(d2r log n) using a probabilistic argument. Here a lower bound of U(2, n)-(n log n) is proved from which U(d, n)-l'I(n log n) for all d is deduce...

On powers of Stieltjes moment sequences, I

For a Bernstein function f the sequence sn = f(1)·. . .·f(n) is a Stieltjes moment sequence with the property that all powers sn, c > 0 are again Stieltjes moment sequences. We prove that sn is Stieltjes determinate for c ≤ 2, but it can be indeterminate for c > 2 as is shown by the moment sequence (n!)c, corresponding to the Bernstein function f(s) = s. Nevertheless there always exists a uniqu...