Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials
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We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C Ψ β,∞ and C Ψ β Hω.
KeywordsPeriodic Function Differentiable Function Trigonometric Polynomial Fixed Generate Asymptotic Equality
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