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Spectral transformations and associated linear functionals of the first kind

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2021-06-28
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MDPI
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Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (P(1)n)n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.
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Spectral Transformation, Darboux Transformations, First Kind Orthogonal Polynomials, Laguerre-Hahn Linear Functional
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García-Ardila, J. C., & Marcellán, F. (2021). Spectral Transformations and Associated Linear Functionals of the First Kind. In Axioms (Vol. 10, Issue 2, p. 107). MDPI AG.