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Plank problems, Hadamard matrices and Lipschitz maps
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Moreno, Oscar Adrian Ortega (2019) Plank problems, Hadamard matrices and Lipschitz maps. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3490285~S15
Abstract
Chapter 1 proves an optimal version of the plank theorem in real Hilbert spaces.
Plank problems are questions concerning coverings of convex sets by planks (regions between two parallel hyperplanes). The problem treated here is related to coverings of unit balls of real Hilbert spaces by collections of planks that are symmetric about the origin. Chapter 2 discusses a connection between two combinatorial designs: 1-factorizations and Hadamard matrices. We consider 1-factorizations of complete graphs that match a given Hadamard matrix. The existence of these factorizations is established for two well-known families of Hadamard matrices: Walsh matrices and certain Paley matrices. Chapter 3 studies Markov type properties for Lp spaces for p 2 (1; 2). The notion of Markov type was introduced by Ball and it describes the evolution of time-reversible Markov chains with a finite number of states on a given Metric space. Ball showed that there is striking connection between this property and the extension of Lipschitz maps. Exploiting this connection, we obtain some results concerning the extension of Lipschitz maps defined on Lp spaces with p 2 [1; 2].
| Item Type: | Thesis or Dissertation (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Stochastic partial differential equations, Hadamard matrices, Lipschitz spaces, Convex sets | ||||
| Official Date: | October 2019 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Ball, Keith M. | ||||
| Sponsors: | Consejo Nacional de Ciencia y Tecnología (Mexico) | ||||
| Extent: | ix, 78 leaves : charts | ||||
| Language: | eng |
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