Wasserstein space over the Wiener space

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.     

A function space -compact space

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.

     

A rigid space homeomorphic to Hilbert space

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 .

     

The space of maps from a locally compact space to a Banach space

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,R^m) is homomorphic to Hilbert spacel ₂. This research is supported by the Science Foundation of Shanxi Province's Scientific Committee     

Fock space on C∞ and Bose-Fock space

In this paper, we introduce the Fock space on ${\mathbb{C}}^{\infty }$ and obtain an isomorphism between the Fock space on ${\mathbb{C}}^{\infty }$ 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.     

A characterization of Bloch space and Besov space

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.     

Hardy space and Bergman space on the Octonions

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.     

A metric space of directions in Minkowski space

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 .     

On the Schwartz space of the basic affine space

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.     

Hardy空间到加权Hardy空间上的复合算子

本文研究了从Hardy空间到加权Hardy空间上的复合算子,并给出此复合算子为有界和紧的条件。     

On the embedding of BV space into Besov-Orlicz space

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.     

Characterization for Beurling-Björck space and Schwartz space

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.

     

可测空间的算子扩张及其上的等价关系

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。     

The space of linear anti-symplectic involutions is a homogenous space

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.     

On Volterra composition operators from Bergman-type space to Bloch-type space

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.