The Hadamard-Schwarz inequality
Given α1,…,αk arbitrary exterior forms in Rn of degree l1,…,lk, does it follow that |α1∧⋯∧αk|≤|α1|⋯|αk| The answer is no in general. However, it is a persistent, popular and even published misconception that the answer is yes. Of course, a routine calculation reveals that there exists at least a con...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/763896 |
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| Summary: | Given α1,…,αk arbitrary exterior forms in Rn of degree l1,…,lk, does it follow that |α1∧⋯∧αk|≤|α1|⋯|αk| The answer is no in general. However, it is a persistent, popular and even published misconception that the answer is yes. Of course, a routine calculation reveals that there exists at least a constant Cn independent of the forms satisfying |α1∧⋯∧αk|≤Cn|α1|⋯|αk| For reasons mentioned in the introduction, we refer to this as the Hadamard-Schwarz inequality. However, what the best constant is, either overall or for the particular numbers l1,…,lk remains well short of clear. |
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| ISSN: | 0972-6802 |