POINTWISE AND NORM CONVERGENCEOF DISTRIBUTIONS,

Abstract

Some results are derived concerning the relation between ordinary pointwise convergence, convergence in the sense of Schwartz distributions (weak convergence), and norm convergence of locally integrable functions by exploiting the notion of analytic continuation for distributions which was recently investigated by H. J. Bremermann and L. Durand III (Jour. Math. Phy. 1961). One of the results is that weak, normed, and almost everywhere pointwise convergence are the same for every dominated sequence provided a certain local equicontinuity in the mean condition is satisfied. A partial converse to this result, showing that norm convergence must imply the local equicontinuity condition and dominance as well as pointwise convergence for some subsequence, is also established. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1963
Accession Number
AD0428782

Entities

People

  • Edward J. Beltrami

Organizations

  • Adelphi University

Tags

DTIC Thesaurus Topics

  • Convergence
  • Weak Convergence

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Military History of the United States in the 20th Century.
  • Operations Research