The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Zero distributions via orthogonality”

Weakly Increasing Zero-Diminishing Sequences

Bakan, Andrew, Craven, Thomas, Csordas, George, Golub, Anatoly (1996)

Serdica Mathematical Journal

Similarity:

The following problem, suggested by Laguerre’s Theorem (1884), remains open: Characterize all real sequences {μk} k=0...∞ which have the zero-diminishing property; that is, if k=0...n, p(x) = ∑(ak x^k) is any P real polynomial, then k=0...n, p(x) = ∑(μk ak x^k) has no more real zeros than p(x). In this paper this problem is solved under the additional assumption of a weak growth condition on the sequence {μk} k=0...∞, namely lim n→∞ | μn |^(1/n) < ∞. More precisely, it is established...