A Refinement of Kolmogorov's Inequality.

Abstract

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 f(t), the (j + 1)th derivative of f(t)) are studied for an arbitrary real t and a prescribed j = 0,...,n-1. A given value of the jth derivative of f(t) determines admissible values for the (j + 1)th derivative of f(t). These values are exactly determined in terms of the Euler spline E sub n(t). Special differentiation formulas of cardinal interpolation type are developed to solve the problem.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1977
Accession Number
ADA046381

Entities

People

  • A. S. Cavaretta Jr.

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Functions (Mathematics)
  • Inequalities
  • Intervals
  • Mathematics
  • Military Research
  • North Carolina
  • Security
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.