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Positivity of Turán determinants for orthogonal polynomials II
Ryszard Szwarc
The polynomials orthogonal on the interval normalized by satisfy Turán's inequality if for and for all …
On a property of random walk polynomials involving Christoffel functions
Erik A. van Doorn, Ryszard Szwarc
Discrete-time birth-death processes may or may not have certain properties known as asymptotic aperiodicity and the strong ratio limit property. In all cases known to us a suitably…
Inverse of Infinite Hankel Moment Matrices
Christian Berg, Ryszard Szwarc
Let denote an indeterminate Hamburger moment sequence and let be the corresponding positive definite Hankel matrix. We consider the questi…
Symmetric moment problems and a conjecture of Valent
Christian Berg, Ryszard Szwarc
In 1998 G. Valent made conjectures about the order and type of certain indeterminate Stieltjes moment problems associated with birth and death processes having polynomial birth and…
A determinant characterization of moment sequences with finitely many mass-points
Christian Berg, Ryszard Szwarc
To a sequence (s_n)_{n\ge 0} of real numbers we associate the sequence of Hankel matrices \mathcal H_n=(s_{i+j}),0\le i,j \le n. We prove that if the corresponding sequence of Hank…
On the order of indeterminate moment problems
Christian Berg, Ryszard Szwarc
For an indeterminate moment problem we denote the orthonormal polynomials by P_n. We study the relation between the growth of the function P(z)=(\sum_{n=0}^\infty|P_n(z)|^2)^{1/2}…