An Analog of Multiplier Sequences for the Set of Totally Positive Sequences
Olga Katkova, Anna Vishnyakova · Zurnal matematiceskoj fiziki analiza geometrii · 2024
To our dear teacher Iossif Vladimirivich Ostrovskii with love and gratitude.We will always remember and admire him not only as an outstanding mathematician and a brilliant teacher, but also as a person of amazing kindness, generosity and nobility.k=0 is called totally positive if all minors of the infinite matrix b j-i ∞ i,j=0 are nonnegative (here b k = 0 for k < 0).In this paper, we investigate the problem of describing the set of sequences (a k ) ∞ k=0 such that for every totally positive sequence (b kis also totally positive.We obtain the description of such sequences (a k ) ∞ k=0 in two cases: when the generating function of the sequence ∞ k=0 a k z k has at least one pole, and when the sequence (a k ) ∞ k=0 has not more than 4 nonzero terms.