Strong Asymptotics of Jacobi-Type Kissing Polynomials

We investigate asymptotic behavior of polynomials $p^ω_n(z)$ satisfying varying non-Hermitian orthogonality relations $\int_{-1}^{1} x^kp^ω_n(x)h(x) e^{\mathrm{i} ωx}\mathrm{d} x =0, \quad k\in\{0,\ldots,n-1\},$ where $h(x) = h^*(x) (1 - x)^α (1 + x)^β, \ ω= λn, \ λ\geq 0$ and $h(x)$ is holomorphic and non-vanishing in a certain neighborhood in the plane. These polynomials are an extension of so-called kissing polynomials ($α= β= 0$) introduced in connection with complex Gaussian quadrature rules with uniform good properties in $ω$.

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