Accession Number : AD0652819

Title :   ON GENERALIZED FUNCTIONS.

Descriptive Note : APL library bulletin translations series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Nasr,Saad K.

Report Date : 11 APR 1967

Pagination or Media Count : 8

Abstract : Let S sub lambda (x) = (K/lambda) exp (- lambda squared/lambda squared -x squared)) if the absolute value of x < lambda; otherwise, S sub lambda (x) = 0; S sub lambda dx = 1. The author defines a g-function as a series (phi sub n) of functions infinitely differentiable on the line such that limit as n approaches infinity, of (phi sub n) * S sub lambda (x) exists for every lambda > o, x > minus infinity but < + infinity. It is found that the g-functions are closely associated with the generalized functions of temple. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, MATHEMATICS), SEQUENCES(MATHEMATICS), THEOREMS, INEQUALITIES, CONVERGENCE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE