Moving finite unit tight frames for \(S^n\)
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| Publicat a: | arXiv.org (Sep 25, 2012), p. n/a |
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| Altres autors: | , |
| Publicat: |
Cornell University Library, arXiv.org
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| Accés en línia: | Citation/Abstract Full text outside of ProQuest |
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| 001 | 2086685894 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 2086685894 | ||
| 045 | 0 | |b d20120925 | |
| 100 | 1 | |a Freeman, Daniel | |
| 245 | 1 | |a Moving finite unit tight frames for \(S^n\) | |
| 260 | |b Cornell University Library, arXiv.org |c Sep 25, 2012 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a Frames for \(\R^n\) can be thought of as redundant or linearly dependent coordinate systems, and have important applications in such areas as signal processing, data compression, and sampling theory. The word "frame" has a different meaning in the context of differential geometry and topology. A moving frame for the tangent bundle of a smooth manifold is a basis for the tangent space at each point which varies smoothly over the manifold. It is well known that the only spheres with a moving basis for their tangent bundle are \(S^1\), \(S^3\), and \(S^7\). On the other hand, after combining the two separate meanings of the word "frame", we show that the \(n\)-dimensional sphere, \(S^n\), has a moving finite unit tight frame for its tangent bundle if and only if \(n\) is odd. We give a procedure for creating vector fields on \(S^{2n-1}\) for all \(n\in\N\), and we characterize exactly when sets of such vector fields form a moving finite unit tight frame. | |
| 653 | |a Data compression | ||
| 653 | |a Bundling | ||
| 653 | |a Manifolds (mathematics) | ||
| 653 | |a Fields (mathematics) | ||
| 653 | |a Signal processing | ||
| 653 | |a Differential geometry | ||
| 653 | |a Coordinates | ||
| 653 | |a Topology | ||
| 700 | 1 | |a Ryan Hotovy | |
| 700 | 1 | |a Martin, Eileen | |
| 773 | 0 | |t arXiv.org |g (Sep 25, 2012), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2086685894/abstract/embedded/L8HZQI7Z43R0LA5T?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/1209.5495 |