共查询到20条相似文献,搜索用时 187 毫秒
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B. Zlatanov 《数学物理学报(B辑英文版)》2011,31(2):576-590
In this note, we investigate the generalized modulus of convexity δ ( λ ) and the generalized modulus smoothness ρ ( λ ) . We obtain some estimates of these moduli for X = lp . We obtain inequalities between WCS coefficient of a K¨othe sequence space X and δ ( λ ) X . We show that, for a wide class of K¨othe sequence spaces X, if for some ε∈ (0, 9 10 ] holds δ X (ε) > 1 3 1 √ 3 2 ε, then X has normal structure. 相似文献
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H. Movahedi-Lankarani R. Wells 《Journal of Mathematical Analysis and Applications》2003,285(1):299-320
The C1-Weierstrass approximation theorem is proved for any compact subset X of a Hilbert space . The same theorem is also proved for Whitney 1-jets on X when X satisfies the following further condition: There exist finite dimensional linear subspaces such that ?n?1Hn is dense in and πn(X)=X∩Hn for each n?1. Here, is the orthogonal projection. It is also shown that when X is compact convex with and satisfies the above condition, then C1(X) is complete if and only if the C1-Whitney extension theorem holds for X. Finally, for compact subsets of , an extension of the C1-Weierstrass approximation theorem is proved for C1 maps with compact derivatives. 相似文献
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The Bohl-Bohr-Amerio-Kadets theorem states that the indefinite integral y=Pφ of an almost periodic (ap) is again ap if y is bounded and the Banach space X does not contain a subspace isomorphic to c0. This is here generalized in several directions: Instead of it holds also for φ defined only on a half-line , instead of ap functions abstract classes with suitable properties are admissible, can be weakened to φ in some “mean” class , then ; here contains all f∈L1loc with in for all h>0 (usually strictly); furthermore, instead of boundedness of y mean boundedness, y in some , or in , ergodic functions, suffices. The Loomis-Doss result on the almost periodicity of a bounded Ψ for which all differences Ψ(t+h)−Ψ(t) are ap for h>0 is extended analogously, also to higher order differences. Studying “difference spaces” in this connection, we obtain decompositions of the form: Any bounded measurable function is the sum of a bounded ergodic function and the indefinite integral of a bounded ergodic function. The Bohr-Neugebauer result on the almost periodicity of bounded solutions y of linear differential equations P(D)y=φ of degree m with ap φ is extended similarly for ; then provided, for example, y is in some with U=L∞ or is totally ergodic and, for the half-line, Reλ?0 for all eigenvalues P(λ)=0. Analogous results hold for systems of linear differential equations. Special case: φ bounded and Pφ ergodic implies Pφ bounded. If all Reλ>0, there exists a unique solution y growing not too fast; this y is in if , for quite general . 相似文献
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