共查询到10条相似文献,搜索用时 109 毫秒
1.
Wang Yangeng 《数学学报(英文版)》1997,13(3):333-336
The space of continuous maps from a topological spaceX to topological spaceY is denoted byC(X,Y) with the compact-open topology. In this paper we prove thatC(X,Y) is an absolute retract ifX is a locally compact separable metric space andY a convex set in a Banach space. From the above fact we know thatC(X,Y) is homomorphic to Hilbert spacel
2 ifX is a locally compact separable metric space andY a separable Banach space; in particular,C(R
n,Rm) is homomorphic to Hilbert spacel
2.
This research is supported by the Science Foundation of Shanxi Province's Scientific Committee 相似文献
2.
Let X be a reduced and irreducible projective variety of dimension d. Let π:X→Y be a separable noetherian normalization of X and ? the canonical morphism Ωd X/k→Ωd L/k. From our main result: $$J_X \varphi (\pi ^* \Omega ^d _{Y/k} ) = \theta _k (X/Y)\varphi (\Omega ^d _{X/k} )$$ we deduce relations among: complementary module C(X/Y), Kähler different θk(X/Y), Dedekind different θD(X/Y), jacobian ideal JK and ω-jacobian ideal \(\tilde J_X\) . 相似文献
3.
《Journal of multivariate analysis》1987,23(1):67-76
A recursive kernel estimate ∑i = 1n YiK⧸(x − Xi)hi)⧸∑j = 1n K((x − Xj)⧸hj) of a regression m(x) = E{Y|X = x} calculated from independent observations (X1, Y1),…, (Xn, Yn) of a pair (X, Y) of random variables is examined. ForE|Y|1 + δ < ∞, δ > 0, the estimate is weakly pointwise consistent for almost all (μ) x ∈ Rd, μ is the probability measure of X, if and only if∑i−1n hid I{hi > ɛ } ⧸ ∑j = 1n hjd → 0 as n → ∞, all ɛ > 0, and∑i = 1∞ hid = ∞, d is the dimension of X. For E|Y|1 + δ < ∞, δ > 0, the estimate is strongly pointwise consistent for almost all (μ) x ∈ Rd, if and only if the same conditions hold. ForE|Y|1 + δ < ∞, δ > 0, weak and strong consistency are equivalent. Similar results are given for complete convergence. 相似文献
4.
Let there be given two F-spaces (X, ∥ ∥*), (Y, ∥ ∥*), X ? Y. A series Σ 1 ∞ xi of elements in X is said to have property O(X, Y) (in the case when X = Y, ∥ ∥ = ∥ ∥*-property O) if perfect boundedness of this series in (X, ∥ ∥) implies its perfect (subseries) convergence in ( Y, ∥ ∥*). Conditions are determined for a series of elements in the space of functions of bounded φ-variation to have property O(X, Y). These conditions are rephrased for the case when convergence with respect to the norm ∥∥ ? v is replaced by modular convergence generated by φ-variation. 相似文献
5.
6.
H. Yoshida 《Israel Journal of Mathematics》1986,54(3):366-380
Given two kinds of functionsf(X) andh(y) defined on them-dimensional Euclidean spaceR m (m≧1) and the set of positive real numbers respectively, we give an estimation of growth of subharmonic functionsu(P) defined onR m+n (n≧1) such that $$u(P) \leqq f\left( X \right)h\left( {\left\| Y \right\|} \right)$$ for anyP=(X, Y),X ∈R m, Y ∈R n, where ‖Y ‖ denotes the usual norm ofY. Using an obtained result, we give a sharpened form of an ordinary Phragmén-Lindelöf theorem with respect to the generalized cylinderD ×R n, with a bounded domainD inR m. 相似文献
7.
Dr. Paul Ressel 《manuscripta mathematica》1974,13(2):143-152
Calling a function f: R + p →R with $$\sum\limits_{i = 1}^n { \sum\limits_{j = 1}^n {\alpha _i \alpha _j } f(t_i + t_j )} \geqslant 0 for all (\alpha _1 ,...,\alpha _n ) \varepsilon R^n ,$$ , (t1,...,tn∈(R + p )n, n∈? positiv semidefinit, the Laplace-transformations of finite nonnegative measures on R + p are charac terised as the continuous bounded positiv semidefinit functions. Let H be a real Hilbertspace. A σ-additive mapping \(M: \mathfrak{B}_ + ^p \to H\) is called an orthogonal measure iff 〈M(A), M(B)?=0 for A∩B=ø. Exactly those mappings Y: R + p →H are Laplacetransformations of H-valued orthogonal measures, which are continuous and bounded and for which ?Y(s), Y(t)? is only a function of s + t. Using this result one obtains a representation theorem for continuous semi-grouphomomorphisms defined on R + p with values in the “unit intervall” of the selfadjoint operators on H. 相似文献
8.
Christopher J. Winfield 《Journal of Geometric Analysis》2001,11(2):343-362
In this article the following class of partial differential operators is examined for local solvability: Let P(X, Y) be a homogeneous polynomial of degree n ≥ 2 in the non-commuting variables X and Y. Suppose that the complex polynomial P(iz, 1) has distinct roots and that P(z, 0) = zn. The operators which we investigate are of the form P(X, Y) where X = δx and Y = δy + xδw for variables (x, y, w) ∈ ?3. We find that the operators P (X, Y) are locally solvable if and only if the kernels of the ordinary differential operators P(iδx, ± x)* contain no Schwartz-class functions other than the zero function. The proof of this theorem involves the construction of a parametrix along with invariance properties of Heisenberg group operators and the application of Sobolev-space inequalities by Hörmander as necessary conditions for local solvability. 相似文献
9.
D. S. Anisimov 《Journal of Mathematical Sciences》2006,139(2):6363-6368
A version of Grothendieck’s inequality says that any bounded linear operator acting from a Banach lattice X to a Banach lattice
Y acts from X(ℓ2) to Y (ℓ2) as well. A similar statement is proved for Hardy-type subspaces in lattices of measurable functions. Namely, let X be a
Banach lattice of measurable functions on the circle, and let an operator T act from the corresponding subspace of analytic
functions XA to a Banach lattice Y or, if Y is also a lattice of measurable functions on the circle, to the quotient space Y/YA. Under certain mild conditions on the lattices involved, it is proved that T induces an operator acting from XA(ℓ2) to Y (ℓ2) or to Y/YA(ℓ2), respectively. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 5–16. 相似文献
10.
Konrad Königsberger 《manuscripta mathematica》1973,8(1):93-109
This article deals with the classification of summands of automorphy on locally trivial fibre spaces E(X, Y), the base space X having the property H1 (X,O)=0 and the fibre Y being a compact Kähler manifold. Further we assume that the structure group is connected and that the transgression H1(Y)H2(X) vanishes. Then every summand of automorphy on E is equivalent to a homomorphism on B1(E) with values in the ring of holomorphic functions on X (theorem I). As a corollary we prove a theorem on the solvability of Cousin-I-Problems on E by additive functions (theorem II).
Meinem verehrten Lehrer KARL STEIN in Dankbarkeit zum 60. Geburtstag gewidmet 相似文献
Meinem verehrten Lehrer KARL STEIN in Dankbarkeit zum 60. Geburtstag gewidmet 相似文献