A sharp version of Henry's theorem on small solutions
β Scribed by S.M.Verduyn Lunel
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 378 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0022-0396
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## Abstract One of the basic results in graph colouring is Brooks' theorem [R. L. Brooks, Proc Cambridge Phil Soc 37 (1941) 194β197], which asserts that the chromatic number of every connected graph, that is not a complete graph or an odd cycle, does not exceed its maximum degree. As an extension o
It is known that, for every (a n ) # l 2 (Z) there exists a function F # C(T) such that |a n | |F (n)| for every n # Z. We prove a noncommutative version: for every matrix A=(a ij ) such that sup i &(a ij ) j & l 2 and sup j &(a ij ) i & l 2 are finite, there exists a matrix (b ij ) defining a bound