On reality property of Wronski maps
E.Mukhin, V.Tarasov, A.Varchenko
TL;DR
This paper proves a reality property for Wronski maps related to quasi-exponentials, extending the B. and M. Shapiro conjecture, using the Bethe ansatz method for the XXX model.
Contribution
It generalizes the B. and M. Shapiro conjecture to quasi-exponentials with real bases and roots, employing the Bethe ansatz technique.
Findings
If roots of the discrete Wronskian are real, simple, and differ by at least 1, then the span has a real basis.
The result extends polynomial space conjectures to quasi-exponentials.
The proof utilizes the Bethe ansatz method for the XXX model.
Abstract
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 result generalizes the B. and M.Shapiro conjecture about spaces of polynomials. The proof is based on the Bethe ansatz method for the XXX model.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Computational Geometry and Mesh Generation