Summary We prove that, for any Tychonoff X, the space Cp(X) is K-analytic if and only if it has a compact cover {Kp: p} such that Kp subset Kq whenever p,q and p q. Applying this result we show that if Cp(X) is K-analytic then Cp(X) is K-analytic as well. We also establish that a space Cp(X) is K-analytic and Baire if and only if X is countable and discrete. 相似文献
We study surfaces M2 in the four-dimensional affine space
equipped with its usual torsion-free connection D and parallel volume form given by the determinant. 相似文献
Let Gn,k be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencescn(β1,β2,…, βk), β1,β2,…, βk= 0,1,2,…, β1+β2 + … +βk ≤n,cn(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + βk) where Δcn(β1,β2,…, βk) =cn(β1 + 1, β2,…, βk)+cn(β1,β2+1,…, βk)+…+cn (β1,β2,…, βk+1) -cn(β1,β2,…, βk). Further, let Πn,k be the set of all symmetric probabilities on {0,1,2,…,k}n. We establish a one-to-one correspondence between the sets Gn,k and Πn,k and use it to formulate and answer interesting questions about both. Assigning to Gn,k the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, βk), 1 ≤ Σβi ≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σm]; the centering constantsc0(β1, β2,…, βk) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inRk. 相似文献
We present sufficient conditions on a Gaussian Mehler semigroup on a reflexive Banach space Eto be induced by a single positive symmetric operator Q \in
, and give a counterexample which shows that this representation theorem is false in every nonreflexive Banach space with a Schauder basis. We also show that the transition semigroup of a Gaussian Mehler semigroup on a separable Banach space Eacts in a pointwise continuous way, uniformly on compact subsets of E, in the space BUC(E) of bounded uniformly continuous real-valued funtions on E. The transition semigroup is shown to be strongly continuous on BUC(E) if and only if S(t) = Ifor all t 0 相似文献
Every Banach space either contains a subspace isomorphic to , or it has an infinite-dimensional closed subspace which is a quotient of a Hereditarily Indecomposable (H.I.) separable Banach space.
In the particular case of , it is shown that the space itself is a quotient of a H.I. space. The factorization of certain classes of operators, acting between Banach spaces, through H.I. spaces is also investigated. Among others it is shown that the identity operator admits a factorization through a H.I. space. The same result holds for every strictly singular operator .
Interpolation methods and the geometric concept of thin convex sets together with the techniques concerning the construction of Hereditarily Indecomposable spaces are used to obtain the above mentioned results. 相似文献
In this paper we study on n a class of smoothly (C) finitely determined vector fields which admit infinite many resonant relations. We give a complete classification of all such vector fields with arbitrarily degenerated nonlinear parts. 相似文献
In the present paper we completely determine the lattice L(NB*) of all varieties of normal bands equipped with an involutorial antiautomorphism as a fundamental operation. 相似文献
For let be the Möbius transformation defined by , and let be the Green's function of the unit disk . We construct an analytic function belonging to for all , , but not belonging to meromorphic in and for any , . This gives a clear difference as compared to the analytic case where the corresponding function spaces ( and ) are same.
A condensation is a one-to-one onto mapping. It is established that, for each -compact metrizable space , the space of real-valued continuous functions on in the topology of pointwise convergence condenses onto a metrizable compactum. Note that not every Tychonoff space condenses onto a compactum.
As a generalization of Wedderburn's classic theorem, it is shown that the multiplicative group of a noncommutative finite dimensional division algebra cannot be finitely generated. Also, the following conjecture is investigated: An infinite non-central normal subgroup of cannot be finitely generated.