On the Problem of Simultaneous Approximation of Functions and Their Derivatives on the Whole Real Axis.
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JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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Considered is the problem of simultaneous approximation on the whole real axis of arbitrary differentiable functions and their derivatives by entire functions of exponential type. S. N. Bernshteins approximation theorem on functions bounded and uniformly continuous between minus infinity, plus infinity is generalized, and an inequality is obtained for the best approximation of derivatives of functions on the whole real axis that is close to the well-known inequality of A. N. Kolmogorov. It is found that upon uniform approximation of arbitrary functions on the whole real axis the constants being considered are appreciably greater in some cases than the corresponding constants in the approximation of 2 pi-periodic functions by trigonometric polynomials. Author
- Theoretical Mathematics