共查询到20条相似文献,搜索用时 31 毫秒
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Shizan Fang Jinghai Shao Karl-Theodor Sturm 《Probability Theory and Related Fields》2010,146(3-4):535-565
The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete characterization of the derivative processes for certain class of absolutely continuous curves. We prove existence of the gradient flow curves for the relative entropy w.r.t. the Wiener measure and identify these gradient flow curves with solutions of the Ornstein–Uhlenbeck evolution equation. 相似文献
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Witold Marciszewski 《Proceedings of the American Mathematical Society》2003,131(6):1965-1969
Assuming that the minimal cardinality of a dominating family in is equal to , we construct a subset of a real line such that the space of continuous real-valued functions on does not admit any continuous bijection onto a -compact space. This gives a consistent answer to a question of Arhangel'skii.
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A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on , and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorphic to Hilbert space. We do this by demonstrating that the first complete rigid space can be modified slightly to be an AR-space (absolute retract), and thus by a theorem of Dobrowolski and Torunczyk is homeomorphic to .
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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
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This research is supported by the Science Foundation of Shanxi Province's Scientific Committee 相似文献
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In this paper, we introduce the Fock space on and obtain an isomorphism between the Fock space on and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on the Bose-Fock space and answer a question in [2]. As a physical application, we study the Gibbs state. 相似文献
7.
E.G. Kwon 《Journal of Mathematical Analysis and Applications》2006,324(2):1429-1437
On the unit disk of the complex plane, a characterization for the membership of Bloch space and analytic Besov space is expressed extending known results. 相似文献
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In this paper, square-integrable Octonion-valued function spaces on R3 and R7 are decomposed into the direct sum of Octonion Hardy and conjugate Hardy spaces, and square-integrable Octonion function spaces on the upper half spaces R + 4 and R + 8 are decomposed into infinity direct sum of subspaces in which the first components are just the Octonion Bergman spaces. The Octonion Hardy Spaces on R3 and R7 are characterized. 相似文献
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Boris V. Dekster 《Journal of Geometry》2004,80(1-2):48-64
A new angular measure in a d-dimensional Minkowski space M was introduced recently. It determines the lengths of rectifiable curves in the (d - 1)-dimensional topological sphere S of all directions in M. Thus, a length structure appears on S. This results in the appropriate intrinsic metric in S. The paper deals with
some properties of the length structure and the resulting metric space S. In particular, it shows that diam S 2 . 相似文献
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Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G / U where U is the group of k-points of a maximal unipotent subgroup of G. In this paper we construct a certain canonical G-invariant space (called the Schwartz space of X) of functions on X, which is an extension of the space of smooth compactly supported functions on X. We show that the space of all elements of , which are invariant under the Iwahori subgroup I of G, coincides with the space generated by the elements of the so called periodic Lusztig basis, introduced recently by G. Lusztig
(cf. [10] and [11]). We also give an interpretation of this space in terms of a certain equivariant K-group (this was also
done by G. Lusztig — cf. [12]). Finally we present a global analogue of , which allows us to give a somewhat non-traditional treatment of the theory of the principal Eisenstein series. 相似文献
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Soon-Yeong Chung Dohan Kim Sungjin Lee 《Proceedings of the American Mathematical Society》1997,125(11):3229-3234
We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space . The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling-Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.
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《Journal of Functional Analysis》2023,284(1):109739
We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple integral inequality involving Young and weight functions. We provide an example with Matuszewska-Orlicz indices of involved Orlicz norm equal to one. The main tool is the molecular decomposition of functions from a BV space. 相似文献
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可测空间的算子扩张及其上的等价关系 总被引:2,自引:0,他引:2
讨论可测空间(U,σU))的两种不同的扩张,使其满足任意并(交)的封闭性,并证明二者是等价的,找到了利用可测空间(U,σ(U))的算子的扩张空间(U,σ^*(U))中的上(下)方逼近算子定义的一个等价关系。 相似文献
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In this note we prove that the space of linear anti-symplectic involutions is the homogenous space ${{{\rm Gl}(n, \mathbb{R})\backslash{\rm Sp}(n)}}$ . This result is motivated by the study of symmetric periodic orbits in the restricted 3-body problem. 相似文献
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Zhi Jie Jiang 《Czechoslovak Mathematical Journal》2011,61(4):993-1005
Let φ be an analytic self-mapping of D and g an analytic function on D. In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the
Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols
g and φ. 相似文献
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