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Spectral transformations and associated linear functionals of the first kind

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URI: https://hdl.handle.net/10016/35030
ISSN: 2075-1680
DOI: https://doi.org/10.3390/axioms10020107
UXXI: AR/0000030759
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Spectral_A_2021.pdf (374.47 KB)
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2021-06-01
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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 ue = (x − c)u with SMOP (Pen)n≥0, we are interested to study the relation between ue and ug(1) , where u (1) is the linear functional for the associated orthogonal polynomials of the first kind (P (1) n )n≥0, and ug(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. Axioms, 10(2), 107.
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