We prove the conjecture of Abbott and Katchalski that for every m ~> 2 there is a positive constant 2,. such that S(K~n ) >~ 2mnd-lS(Ka~ -1) where S(Ka~) is the length of the longest snake (cycle without chords) in the cartesian product K~ of d copies of the complete graph Kin. As a corollary, we co
On constructing bases in certain complete spaces
β Scribed by J.M Aarts; D.J Lutzer
- Publisher
- Elsevier Science
- Year
- 1976
- Weight
- 271 KB
- Volume
- 79
- Category
- Article
- ISSN
- 1385-7258
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π SIMILAR VOLUMES
By using a norm generated by the error series of a sequence of interpolation polynomials, we obtain in this paper ~ertain Banach spaces. A relation between these spaces and the space (Co, S) with norm generated by the error series of the best polynomial approximations (minimax series) is established
In the present paper we consider periodic spline systems in order to obtain SCHAUDEB bases for the real HARDY spaces Hp(T) (0 < p 5 1) defined on the one-dimensional torus T . In a recent note [la] we have shown that the periodic FFLANKLIN system forms a basis in H J T ) if 112 < p < 1. Obviously,