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article · Defense Technical Information Center (DTIC) · 1976

Derivatives, Differences, Multiple Fourier Kernels.

Detian Liu, Louise Young

Cited by 0Abstract and details only

Abstract

Identities and inequalities for Fourier kernels and for difference operators are related to a geometric series identity. The resulting machinery is applied to obtain, in the approximation theory for ordinary or partial derivatives of any order, necessary and sufficient conditions in place of classical sufficient conditions. Alternative formulations are given in terms of Tauberian Theorems, and in terms of Schwartz distributions. The results are achieved by making use, as in L. C. Young's papers on Stochastic integrals and the like, of pairs of estimate functions in place of the classical higher moduli of continuity.

Cite this paper

APA 7

Liu, D., & Young, L. (1976). Derivatives, Differences, Multiple Fourier Kernels. Defense Technical Information Center (DTIC).

MLA 9

Liu, Detian, and Louise Young. “Derivatives, Differences, Multiple Fourier Kernels.” Defense Technical Information Center (DTIC), 1976.

Chicago

Liu, Detian, and Louise Young. 1976. “Derivatives, Differences, Multiple Fourier Kernels.” Defense Technical Information Center (DTIC).

Harvard

Liu, D. and Young, L. (1976) ‘Derivatives, Differences, Multiple Fourier Kernels’, Defense Technical Information Center (DTIC).

BibTeX
@article{liu1976derivatives,
  title = {{Derivatives, Differences, Multiple Fourier Kernels.}},
  author = {Liu, Detian and Young, Louise},
  journal = {Defense Technical Information Center (DTIC)},
  year = {1976}
}

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