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Bounds on orthogonal polynomials and separation of their zeros

https://doi.org/10.4171/JST/408

Levin, Eli ; Lubinsky, Doron S. ( January 2022 , Journal of Spectral Theory)

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Variance of real zeros of random orthogonal polynomials for varying and exponential weights

https://doi.org/10.1214/22-EJP802

Lubinsky, Doron S. ; Pritsker, Igor E. ( January 2022 , Electronic Journal of Probability)

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On Uniform Convergence of Diagonal Multipoint Pad� Approximants For Entire Functions

Lubinsky, Doron S ( January 2019 , Constructive approximation)

We prove that for most entire functions f in the sense of category, a strong form of the Baker-Gammel-Wills Conjecture holds. More precisely, there is an inÖnite sequence S of positive integers n, such that given any r > 0, and multipoint PadÈ approximants Rn to f with interpolation points in fz : jzj rg, fRngn2S converges locally uniformly to f in the plane. The sequence S does not depend on r, nor on the interpolation points. For entire functions with smooth rapidly decreasing coe¢ cients, full diagonal sequences of multipoint PadÈ approximants converge.
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