Citation
Pfeffer, Allen Michael (1966) On Certain Discrete Inequalities and Their Continuous 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.)) | ||||||
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| Subject Keywords: | (Mathematics) | ||||||
| Degree Grantor: | California Institute of Technology | ||||||
| Division: | Physics, Mathematics and Astronomy | ||||||
| Major Option: | Mathematics | ||||||
| Thesis Availability: | Public (worldwide access) | ||||||
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| Defense Date: | 4 November 1965 | ||||||
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| 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: | INVALID USER | ||||||
| Deposited On: | 02 Oct 2015 19:49 | ||||||
| Last Modified: | 07 Mar 2024 22:22 |
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