The Christoffel-Darboux Kernel

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A review of the uses of the CD kernel in the spectral theory of orthogonal polynomials, concentrating on recent results.

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Asymptotics of Orthogonal Polynomials for a Weight with a Jump on [−1,1] (2009, methodology): “Notice that combining ideas from [16] and [18] we can use (23) to arrive at the same conclusions about the spacing of zeros of Pn’s as we did at the end of Subsection 3.”
EQUILIBRIUM MEASURES AND CAPACITIES IN SPECTRAL THEORY (2007, background): “But unlike Rakhmanov’s theorem which is only known for a few other E’s (see [29, 90 ] and the discussion in Section 8), this weaker version holds very generally.”
The Smallest Eigenvalue of Hankel Matrices (2009, background): “Collar [12], has been rediscovered several times, see [3, 17].”