This research demonstrates total positivity conditions in analytic functions using symmetric functions and Cauchy identities.
This paper studies the bidiagonal factorization of the collocation matrices of analytic bases using symmetric functions. Explicit formulas for their initial minors are derived in terms of Schur functions. The structure of these formulas permits establishing sufficient conditions for the total positivity of generic systems of analytic functions. In addition, they have been found to lead to generalizations of the Cauchy identity for certain families of functions.
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Díaz et al. (2026) studied this question.
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