LetCp(X) be the space of all continuous real-valued functions on a space X , with the topology of pointwise convergence. In this paper we show thatCp(X) is not domain representable unless X is discrete for a class of spaces that includes all pseudo-radial spaces and all generalized ordered spaces. This is a first step toward our conjecture that if X is completely regular, then Cp(X) is domain r...

We show that if the space `∞/c0 contains an isometric copy of every function space over a first countable compactum or every function space over a Corson copactum of weight not exceeding the continuum then every subset of R belongs to the σfield generated by sets of the form A1×A2.We prove a similar result about isomorphic rather than isometric embeddings into `∞/c0 in terms of the σ-field of s...

We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0, 3]. We compare these spaces and characterize them in terms of Daubechies wavelets.

Given topological spaces Xt ÜT, and F and a function h from XXT to F which is continuous in x for each fixed ty there is associated with h a function h* from I t o F = F x , the space whose elements are the continuous functions from X to F. The function h* is defined as follows: h*(t)=ht, where ht(x)~h(x} t) for every x in X. The correspondence between h and h* is obviously one-to-one. Although...

In this survey we review the recently developed theory of anisotropic spaces and representations of functions based on anisotropic multilevel ellipsoid covers (dilations) of Rn. We also exhibit the relations of the ellipsoid cover approach to earlier concepts of anisotropic structures as well as to the framework of general spaces of homogeneous type. A number of open problems are presented and ...

We want to recover a continuous function f : (0, 1)d → C using only its function values. Let us assume, that f is from the unit ball of some function space (for example a fractional Sobolev space or a Besov space) and the precision of the reconstruction is measured in the norm of another function space of this type. We describe the rate of convergence of the optimal sampling method (linear as w...

Introduction IN a previous paper (4) I defined ten product topologies o n l x T . In this paper five of these products are applied to problems on function spaces. All spaces will be Hausdorff spaces. The exponential law for function spaces with the compact-open topology is discussed in § 1. The main result (Theorem 1.6) is that the spaces X and (X) are homeomorphic for all X, Y, Z (in this pape...

We give a condition for a Borel measure on R which is sufficient for the validity of an AD-type correlation inequality in the function space In [1] was proved that if φ1, φ2, φ3, φ4 are bounded real non negative measurable functions on the space with measure (Rn,B, μ) which satisfy for all x̄, ȳ ∈ R the following inequality φ1(x̄)φ2(ȳ) ≤ φ3(x̄ ∨ ȳ)φ4(x̄ ∧ ȳ) a.s., (1) then ∫ φ1(x̄)μ(dx̄) ∫ φ2(x̄)μ(dx̄)...

ing the above, for a (not necessarily countable) family . . . φ2 // B1 φ1 // Bo of Banach spaces with continuous linear transition maps as indicated, not recessarily requiring the continuous linear maps to be injective (or surjective), a (projective) limit limiBi is a topological vector space with continuous linear maps limiBi → Bj such that, for every compatible family of continuous linear map...