Correction to a Theorem on Total Positivity
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 281-284
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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.
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
@article{10_4153_CMB_2006_029_0,
author = {Ragnarsson, Carl Johan and Suen, Wesley Wai and Wagner, David G.},
title = {Correction to a {Theorem} on {Total} {Positivity}},
journal = {Canadian mathematical bulletin},
pages = {281--284},
year = {2006},
volume = {49},
number = {2},
doi = {10.4153/CMB-2006-029-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-029-0/}
}
TY - JOUR AU - Ragnarsson, Carl Johan AU - Suen, Wesley Wai AU - Wagner, David G. TI - Correction to a Theorem on Total Positivity JO - Canadian mathematical bulletin PY - 2006 SP - 281 EP - 284 VL - 49 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-029-0/ DO - 10.4153/CMB-2006-029-0 ID - 10_4153_CMB_2006_029_0 ER -
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