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Real-valued semiclassical approximation for the asymptotics with complex-valued phases and its application to multiple orthogonal Hermite polynomials A. V. Tsvetkova Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow |
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Abstract: The multiple orthogonal Hermite polynomials \begin{gather*} H_{n_1+1,n_2}(z,a)=(z+a)H_{n_1,n_2}(z,a)-\frac{1}{2} \left(n_1H_{n_1-1,n_2}(z,a)+n_2H_{n_1,n_2-1}(z,a)\right),\\ H_{n_1,n_2+1}(z,a)=(z-a)H_{n_1,n_2}(z,a)-\frac{1}{2} \left(n_1H_{n_1-1,n_2}(z,a)+n_2H_{n_1,n_2-1}(z,a)\right). \end{gather*} We construct the uniform Plancherel–Rotach-type asymptotics of diagonal polynomials The discussed approach can be applied to construct asymptotics for a wide class of orthogonal polynomials. The idea of the method is to introduce a small artificial parameter The talk is based on the joint work with A. I. Aptekarev (Keldysh Institute of Applied Mathematics RAS), S. Yu. Dobrokhotov (Ishlinsky Institute for Problems in Mechanics RAS) and D. N. Tulyakov (Keldysh Institute of Applied Mathematics RAS). Language: English Website: https://us02web.zoom.us/j/8618528524?pwd=MmxGeHRWZHZnS0NLQi9jTTFTTzFrQT09 * Zoom conference ID: 861 852 8524 , password: caopa |