共查询到20条相似文献,搜索用时 31 毫秒
1.
Let W and V be centrally symmetric sets in a normed space X. The relative Kolmogorov n-width of W relative to V in X is defined by
2.
Biagio Ricceri 《Topology and its Applications》2006,153(17):3308-3312
In this paper, we establish some minimax theorems, of purely topological nature, that, through the variational methods, can be usefully applied to nonlinear differential equations. Here is a (simplified) sample: Let X be a Hausdorff topological space, I⊆R an interval and . Assume that the function Ψ(x,⋅) is lower semicontinuous and quasi-concave in I for all x∈X, while the function Ψ(⋅,q) has compact sublevel sets and one local minimum at most for each q in a dense subset of I. Then, one has
3.
Bogdan Batko 《Journal of Mathematical Analysis and Applications》2008,340(1):424-432
Let f:S→X map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability of Dhombres' equation
4.
C. Angosto 《Topology and its Applications》2007,155(2):69-81
Given a metric space X and a Banach space (E,‖⋅‖) we study distances from the set of selectors Sel(F) of a set-valued map to the space B1(X,E) of Baire one functions from X into E. For this we introduce the d-τ-semioscillation of a set-valued map with values in a topological space (Y,τ) also endowed with a metric d. Being more precise we obtain that
5.
Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X1+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,
6.
Ohad Giladi 《Journal of Functional Analysis》2011,260(1):164-194
It is shown that if (X,‖⋅X‖) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer such that for every we have
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8.
Bogdan Batko 《Journal of Mathematical Analysis and Applications》2008,339(1):303-311
Let map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability of the following alternative functional equation
9.
Markus Biegert 《Journal of Mathematical Analysis and Applications》2009,358(2):294-306
The purpose of this article is to define a capacity on certain topological measure spaces X with respect to certain function spaces V consisting of measurable functions. In this general theory we will not fix the space V but we emphasize that V can be the classical Sobolev space W1,p(Ω), the classical Orlicz-Sobolev space W1,Φ(Ω), the Haj?asz-Sobolev space M1,p(Ω), the Musielak-Orlicz-Sobolev space (or generalized Orlicz-Sobolev space) and many other spaces. Of particular interest is the space given as the closure of in W1,p(Ω). In this case every function u∈V (a priori defined only on Ω) has a trace on the boundary ∂Ω which is unique up to a Capp,Ω-polar set. 相似文献
10.
Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆Vi-1+Vi+Vi+1 for 0?i?d, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W, A∗W⊆W, W≠0, W≠V. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide. The pair A,A∗ is called sharp whenever . It is known that if F is algebraically closed then A,A∗ is sharp. In this paper we classify up to isomorphism the sharp tridiagonal pairs. As a corollary, we classify up to isomorphism the tridiagonal pairs over an algebraically closed field. We obtain these classifications by proving the μ-conjecture. 相似文献
11.
Let K denote a field and let V denote a vector space over K with finite positive dimension.We consider a pair of K-linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆Vi-1+Vi+Vi+1 for 0?i?d, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W,A∗W⊆W,W≠0,W≠V.We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide.In this paper we show that the following (i)-(iv) hold provided that K is algebraically closed: (i) Each of has dimension 1.(ii) There exists a nondegenerate symmetric bilinear form 〈,〉 on V such that 〈Au,v〉=〈u,Av〉 and 〈A∗u,v〉=〈u,A∗v〉 for all u,v∈V.(iii) There exists a unique anti-automorphism of End(V) that fixes each of A,A∗.(iv) The pair A,A∗ is determined up to isomorphism by the data , where θi (resp.) is the eigenvalue of A (resp.A∗) on Vi (resp.), and is the split sequence of A,A∗ corresponding to and . 相似文献
12.
Pierre Gillibert 《Journal of Pure and Applied Algebra》2010,214(8):1306-1318
We denote by the semilattice of all compact congruences of an algebra A. Given a variety V of algebras, we denote by the class of all semilattices isomorphic to for some A∈V. Given varieties V and W of algebras, the critical point of V under W is defined as . Given a finitely generated variety V of modular lattices, we obtain an integer ?, depending on V, such that for any n≥? and any field F.In a second part, using tools introduced in Gillibert (2009) [5], we prove that:
13.
Fernanda Botelho James E. Jamison 《Journal of Mathematical Analysis and Applications》2011,381(2):821-832
For a Banach space E and a compact metric space (X,d), a function F:X→E is a Lipschitz function if there exists k>0 such that
14.
Let p∈[1,2) and α, ε>0 be such that α∈(p−1,1−ε). Let V, W be two Euclidean spaces. Let Ωp(V) be the space of continuous paths taking values in V and with finite p-variation. Let k∈N and be a Lip(k+α+ε) map in the sense of E.M. Stein [Stein E.M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970]. In this paper we prove that the Itô map, defined by I(x)=y, is a local map (in the sense of Fréchet) between Ωp(V) and Ωp(W), where y is the solution to the differential equation
15.
Let (X,d,μ) be a metric measure space. For ∅≠R⊆(0,∞) consider the Hardy-Littlewood maximal operator
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Piotr Niemiec 《Topology and its Applications》2007,154(3):655-664
The aim of this paper is to answer the following question: let (X,?) and (Y,d) be metric spaces, let A,B⊂Y be continuous images of the space X and let be a fixed continuous surjection. When is the inequality
17.
A cone space is a complete metric space (X,d) with a pair of functions cs,cu:X×X→R, such that there exists K>0 satisfying
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For a bounded function f from the unit sphere of a closed subspace X of a Banach space Y, we study when the closed convex hull of its spatial numerical range W(f) is equal to its intrinsic numerical range V(f). We show that for every infinite-dimensional Banach space X there is a superspace Y and a bounded linear operator such that . We also show that, up to renormig, for every non-reflexive Banach space Y, one can find a closed subspace X and a bounded linear operator T∈L(X,Y) such that .Finally, we introduce a sufficient condition for the closed convex hull of the spatial numerical range to be equal to the intrinsic numerical range, which we call the Bishop-Phelps-Bollobás property, and which is weaker than the uniform smoothness and the finite-dimensionality. We characterize strong subdifferentiability and uniform smoothness in terms of this property. 相似文献
20.
A. Jiménez-Vargas 《Journal of Mathematical Analysis and Applications》2008,337(2):984-993
Given a real number α∈(0,1) and a metric space (X,d), let Lipα(X) be the algebra of all scalar-valued bounded functions f on X such that