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- Title
Reality Property of Discrete Wronski Map with Imaginary Step.
- Authors
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
- Abstract
For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2 h. We prove that if the coefficients of the discrete Wronskian are real and the imaginary parts of its roots are bounded by | h|, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result is a generalization of the statement of the B. and M. Shapiro conjecture on spaces of polynomials. The proof is based on the Bethe ansatz for the XXX model.
- Subjects
WRONSKIAN determinant; EXPONENTS; ROOTS of equations; POLYNOMIALS; BETHE-ansatz technique; MANY-body problem; MATHEMATICAL physics
- Publication
Letters in Mathematical Physics, 2012, Vol 100, Issue 2, p151
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-011-0521-x