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1. CMB 2006 (vol 49 pp. 281)
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Correction to a Theorem on Total Positivity A well-known theorem states that if $f(z)$ generates a PF$_r$
sequence then $1/f(-z)$ generates a PF$_r$ sequence. We give two
counterexamples
which show that this is not true, and give a correct version of the theorem.
In the infinite limit the result is sound: if $f(z)$ generates a PF
sequence then $1/f(-z)$ generates a PF sequence.
Keywords:total positivity, Toeplitz matrix, Pólya frequency sequence, skew Schur function Categories:15A48, 15A45, 15A57, 05E05 |