On Certain Discrete Inequalities and Their Continuous Analogues

Author: Pfeffer, Allen Michael

Year: 1966

Degree: Dissertation (Ph.D.)

Advisor: Todd, John

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/H48H-1911

Abstract

In a 1955 paper, Ky Fan, Olga Taussky, and John Todd presented discrete analogues of inequalities of Wirtinger type, and by taking limits they were able to recover the continuous inequalities. We generalize their techniques to mixed and higher derivatives and inequalities with weight functions in the integrals. We have also considered analogues of inequalities of Müller and Redheffer and have used these inequalities to derive a necessary and sufficient condition on ordered pairs of numbers so that the first number is the square norm of the kth derivative of some periodic function and the second number is the square norm of the mth derivative of the same periodic function.

Files