A Refinement of Kolmogorov's Inequality.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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For any n-times differentiable function f with uniform bounds on f and the nth derivative of f, the pair of values the jth derivative of ft, the j 1th derivative of ft are studied for an arbitrary real t and a prescribed j 0,...,n-1. A given value of the jth derivative of ft determines admissible values for the j 1th derivative of ft. These values are exactly determined in terms of the Euler spline E sub nt. Special differentiation formulas of cardinal interpolation type are developed to solve the problem.
- Theoretical Mathematics