On reality property of Wronski maps
Confluentes Mathematici, Volume 1 (2009) no. 2, pp. 225-247.

We prove that if all roots of the discrete Wronskian with step 1 of a set of quasi-exponentials with real bases are real, simple and differ by at least 1, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This theorem generalizes the statement of the B. and M. Shapiro conjecture about spaces of polynomials.

The proof is based on the Bethe ansatz method for the XXX model.

Published online:
DOI: 10.1142/S1793744209000092
Evgenii Mukhin 1; Vitaly Tarasov 1; Aleksandr Varchenko 1

1
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Evgenii Mukhin; Vitaly Tarasov; Aleksandr Varchenko. On reality property of Wronski maps. Confluentes Mathematici, Volume 1 (2009) no. 2, pp. 225-247. doi : 10.1142/S1793744209000092. https://cml.centre-mersenne.org/articles/10.1142/S1793744209000092/

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