摘要
Let Wβ（x） = exp（-1/2｜x｜^β） be the Freud weight and pn（x） ∈ ∏n be the sequence of orthogonal polynomials with respect to W^2β（x）, that is,∫^∞ -∞pn（x）pm（x）W^2β（x）dx{0,n≠m,1,n=m.It is known that all the zeros of pn（x） are distributed on the whole real line. The present paper investigates the convergence of Grfinwald interpolatory operators based on the zeros of orthogonal polynomials for the Freud weights. We prove that, if we take the zeros of Freud polynomials as the interpolation nodes, thenGn（f,x）→ f（x）,n→∞holds for every x ∈ （-∞, ∞）, where f（x） is any continous function on the real line satisfying ｜f（x）｜ = O（exp（1/2｜x｜^β）.
Let Wβ（x） = exp（-1/2｜x｜^β） be the Freud weight and pn（x） ∈ ∏n be the sequence of orthogonal polynomials with respect to W^2β（x）, that is,∫^∞ -∞pn（x）pm（x）W^2β（x）dx{0,n≠m,1,n=m.It is known that all the zeros of pn（x） are distributed on the whole real line. The present paper investigates the convergence of Grfinwald interpolatory operators based on the zeros of orthogonal polynomials for the Freud weights. We prove that, if we take the zeros of Freud polynomials as the interpolation nodes, thenGn（f,x）→ f（x）,n→∞holds for every x ∈ （-∞, ∞）, where f（x） is any continous function on the real line satisfying ｜f（x）｜ = O（exp（1/2｜x｜^β）.
基金
Open Funds(No.PCN0613) of State Key Laboratory of Oil and Gas Reservoir and Exploitation(Southwest Petroleum University)
the Foundation of Education of Zhejiang Province(No.Kyg091206029)
