【摘 要】
:
The classical A.Markov inequality establishes a relation between the maximum modulus or the L∞([-1,1])norm of a polynomial Qn and of its derivative:‖Qn‖≤Mnn
【机 构】
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KeldyshInstituteofAppliedMathematics,RussianAcademyofSciences
【出 处】
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International Conference on Orthogonal Polynomials,Integrabl
论文部分内容阅读
The classical A.Markov inequality establishes a relation between the maximum modulus or the L∞([-1,1])norm of a polynomial Qn and of its derivative:‖Qn‖≤Mnn2‖Qn‖,where the constant Mn = 1 is sharp.The limiting behavior of the sharp constants Mn for this inequality,considered in the space L2([-1,1],ω(α,β))with respect to the classical Jacobi weight ω(α,β)(x):=(1-x)α(x+1)β,is studied.We prove that,under a technical condition |α-β| < 4,the limit is limn→∞Mn = 1/(2jv)where jv is the smallest zero of the Bessel function Jv(x)and 2v = min(α,β)-1.
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