Abstract:
An estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space is obtained. It is shown that, under a certain choice of the sequence of multi-indices, the interpolating polynomials converge to the interpolated function and the rate of convergence is of the order of the best approximation of this function by algebraic polynomials in this space.
Keywords:Lagrange interpolation operator, weighted Sobolev space, interpolating polynomials, approximation by algebraic polynomials, Chebyshev polynomials, Fourier coefficients of a polynomial.
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