虚步长离散Wronski映射的实在性
Reality property of discrete Wronski map with imaginary step
摘要：
对于一组具有实指数的拟指数，我们考虑具有纯虚步长2h的离散朗斯基（也称为Casorati行列式）。我们证明了如果离散Wronskian的系数是实的，并且对于它的每一个根，虚部至多是|h|，那么这组拟指数的复跨度有一个由实系数的拟指数组成的基。这个结果是B.和M.多项式空间上的Shapiro猜想。证明基于XXX模型的Bethe检验。
英文摘要：
For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2h. We prove that if the coefficients of the discrete Wronskian are real and for every its roots the imaginary part is at most |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.
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