Geodesic
Correction to a Theorem on Total Positivity
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 281-284

Voir la notice de l'article provenant de la source Cambridge University Press

A well-known theorem states that if $f\left( z \right)$ generates a $\text{P}{{\text{F}}_{r}}$ sequence then $1/f\left( -z \right)$ generates a $\text{P}{{\text{F}}_{r}}$ 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 $f\left( z \right)$ generates a $\text{PF}$ sequence then $1/f\left( -z \right)$ generates a $\text{PF}$ sequence.
DOI : 10.4153/CMB-2006-029-0
Mots-clés : 15A48, 15A45, 15A57, 05E05, Total positivity, Toeplitz matrix, Pólya frequency sequence, skew Schur function 
Ragnarsson, Carl Johan; Suen, Wesley Wai; Wagner, David G. Correction to a Theorem on Total Positivity. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 281-284. doi: 10.4153/CMB-2006-029-0
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