It is well known that the Taylor series of every function in the Fock space converges in norm when 1 < p < ∞. It is also known that this is no longer true when p = 1. In this note we consider the case 0 < p < 1 and show that the Taylor series of functions in do not necessarily converge “in norm”.
In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category . Finally,...
We first show that the Gaussian integral means of (with respect to the area measure ) is a convex function of on when . We then prove that the weighted integral means and of the mixed area and the mixed length of and , respectively, also have the property of convexity in the case of . Finally, we show with examples that the range is the best possible.
Let (A,α) and (B,β) be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: R-smash products . Moreover, necessary and sufficient conditions for to be a cobraided Hom-Hopf algebra are given.
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