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On certain discrete inequalities and their continous analogues

Citation

Pfeffer, Allen Michael (1966) On certain discrete inequalities and their continous analogues. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/H48H-1911. https://resolver.caltech.edu/CaltechTHESIS:10012015-134922597

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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Todd, John
Thesis Committee:
  • Unknown, Unknown
Defense Date:4 November 1965
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
CaltechUNSPECIFIED
Record Number:CaltechTHESIS:10012015-134922597
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:10012015-134922597
DOI:10.7907/H48H-1911
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9186
Collection:CaltechTHESIS
Deposited By: Leslie Granillo
Deposited On:02 Oct 2015 19:49
Last Modified:21 Dec 2019 02:07

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