Certain negative results on consequences of the first kind multipliers
It is proved that the composition of a polynomial with a multiplier sequence of the first kind may lead to a diminishing of the number of real roots of this polynomial and that the reciprocals of the moments of a nonnegative function on [0, 1] need not form a multiplier sequence of the first kind. O...
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| Datum: | 1992 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8098 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | It is proved that the composition of a polynomial with a multiplier sequence of the first kind may lead to a diminishing of the number of real roots of this polynomial and that the reciprocals of the moments of a nonnegative function on [0, 1] need not form a multiplier sequence of the first kind. On the basis of these facts one establishes the inaccuracy of the solution, obtained by T. Craven and G. Csordas, to S. Karlin's problem on the characterization of linear transformations that do not increase the number of zeros and also the incorrectness of M. Kostova's certain results, given in L. Iliev's monograph “Laguerre entire functions” (Sofia, 1987).
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