Browsing by Subject "strong asymptotics"

Now showing 1 - 3 of 3
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    Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-Type Weight
    (Springer, 2020) Barhoumi, Ahmad; Yattselev, Maxim L.; Mathematical Sciences, School of Science
    We investigate asymptotic behavior of polynomials Qn(z) satisfying non-Hermitian orthogonality relations ∫ΔskQn(s)ρ(s)ds=0,k∈{0,…,n−1}, where Δ:=[−a,a]∪[−ib,ib], a,b>0, and ρ(s) is a Jacobi-type weight.
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    On LR2-best rational approximants to Markov functions on several intervals
    (Elsevier, 2022-06) Yattselev, Maxim L.; Mathematical Sciences, School of Science
    Let f(z)=∫(z−x)−1dμ(x), where μ is a Borel measure supported on several subintervals of (−1,1) with smooth Radon–Nikodym derivative. We study strong asymptotic behavior of the error of approximation (f−rn)(z), where rn(z) is the LR2-best rational approximant to f(z) on the unit circle with n poles inside the unit disk.
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    On Multipoint Padé Approximants whose Poles Accumulate on Contours that Separate the Plane
    (Springer, 2021-11) Yattselev, M. L.; Mathematical Sciences, School of Science
    In this note we consider asymptotics of the multipoint Padé approximants to Cauchy integrals of analytic non-vanishing densities defined on a Jordan arc connecting -1 and 1. We allow for the situation where the (symmetric) contour attracting the poles of the approximants does separate the plane.