All maps of type are boundary maps

Let be a continuous map of an interval into itself having periodic points of period for all and no other periods. It is shown that every neighborhood of contains a map such that the set of periods of the periodic points of is finite. This answers a question posed by L. S. Block and W. A. Coppel.

     

Complemented isometric copies of in dual Banach spaces

Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .

     

Copies of in topological Riesz spaces

The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of or .

     

Irreducible representations of the Cuntz algebra

In this paper, we establish formulas for the configuration of a special class of irreducible representations of the Cuntz algebra , . These irreducible representations arise as subrepresentations of naturally occurring representations of acting in and arise from consideration of multiresolution wavelet filters.

     

The

In this paper we analyze the localization of , the fiber of the double suspension map , with respect to . If four cells at the bottom of , the th extended power spectrum of the Moore spectrum, are collapsed to a point, then one obtains a spectrum . Let be the James-Hopf map followed by the collapse map. Then we show that the secondary suspension map has a lifting to the fiber of and this lifting is shown to be a -periodic equivalence, hence an -equivalence.

     

Paranormal spaces under

We prove that paranormal spaces of character are -
collectionwise Hausdorff assuming the set-theoretic principle . This gives an affirmative answer to problem 197 in Problems I wish I could solve, by W. S. Watson (Open Problems in Topology (1990), 37-76).

     

Spaces of type and the Hankel convolution

In this paper we introduce new function spaces that are denoted by , -1/2$"> and and that are spaces of type where the Hankel convolution and the Hankel transformation are defined. The spaces will play the same role in the Hankel setting that the spaces play in the theory of Fourier transformation.     

Weak type estimates for cone multipliers on

We consider operators associated with the Fourier multipliers and show that is of weak type on , , for the critical value .

     

The -PIP and integrability of a single function

Two examples are given that answer in the negative the following question asked by E. M. Bator: If is bounded and weakly measurable and for each in there is a bounded sequence in such that a.e., does it follow that is Pettis integrable?

     

Every nonreflexive subspace of fails the fixed point property

The main result of this paper is that every nonreflexive subspace of fails the fixed point property for closed, bounded, convex subsets of and nonexpansive (or contractive) mappings on . Combined with a theorem of Maurey we get that for subspaces of , is reflexive if and only if has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open.

     

从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)$的加权复合算子

设$u \in H(D), \ \phi$为$D$上的解析自映射,定义$H(D)$上的加权复合算子为$u C_{\phi}(f)=$$uf\circ\phi$, \ $f\in H(D)$.本文得到了从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)\ (A_{0}^{\infty}(\varphi))$的加权复合算子$u C_{\phi}$的有界性和紧性的充要条件.     

BEM with linear complexity for the classical boundary integral operators

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one to choose the order of the numerical approximations much lower than for the classical formulations. Low-order discretisations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU time grow only linearly with respect to the number of unknowns.

     

A separable non-remainder of

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.

     

On the correlations of directions in the Euclidean plane

Let denote the repartition of the -level correlation measure of the finite set of directions , where is the fixed point and is an integer lattice point in the square . We show that the average of the pair correlation repartition over in a fixed disc converges as . More precisely we prove, for every and , the estimate

We also prove that for each individual point , the -level correlation diverges at any point as , and we give an explicit lower bound for the rate of divergence.

     

The expected norm of random polynomials

The results of this paper concern the expected norm of random polynomials on the boundary of the unit disc (equivalently of random trigonometric polynomials on the interval ). Specifically, for a random polynomial

let

Assume the random variables , are independent and identically distributed, have mean 0, variance equal to 1 and, if 2$">, a finite moment . Then

and

as .

In particular if the polynomials in question have coefficients in the set (a much studied class of polynomials), then we can compute the expected norms of the polynomials and their derivatives

and

This complements results of Fielding in the case, Newman and Byrnes in the case, and Littlewood et al. in the case.

     

-summand vectors in Banach spaces

The aim of this paper is to study the set of all -summand vectors of a real Banach space . We provide a characterization of -summand vectors in smooth real Banach spaces and a general decomposition theorem which shows that every real Banach space can be decomposed as an -sum of a Hilbert space and a Banach space without nontrivial -summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces.

     

A universal continuum of weight

We prove that every continuum of weight  is a continuous image of the Cech-Stone-remainder  of the real line. It follows that under  the remainder of the half line is universal among the continua of weight  -- universal in the `mapping onto' sense.

We complement this result by showing that 1) under  every continuum of weight less than  is a continuous image of , 2) in the Cohen model the long segment of length  is not a continuous image of , and 3)  implies that is not a continuous image of , whenever  is a -saturated ultrafilter.

We also show that a universal continuum can be gotten from a -saturated ultrafilter on , and that it is consistent that there is no universal continuum of weight  .

     

基于完备BR0-代数的全蕴涵三I算法

研究了基础$BR_0$-代数的性质和基于完备基础$BR_0$-代数的全蕴涵三I算法,对一般蕴涵算子给出了三I算法解存在的一个充分条件,并将结果应用于$R_0$-单位区间$\overline{W}$,不但极大的简化了$R_0$-单位区间$\overline{W}$的$R_0$-型$\alpha$-三I算法结果的证明,而且使其证明过程与相应的模糊命题演算系统结合起来,说明了$R_0$-型三I算法是与$B{\cal L}^*$系统相匹配的模糊推理方法.     

The index of a critical point for densely defined operators of type in Banach spaces

The purpose of this paper is to demonstrate that it is possible to define and compute the index of an isolated critical point for densely defined operators of type acting from a real, reflexive and separable Banach space into This index is defined via a degree theory for such operators which has been recently developed by the authors. The calculation of the index is achieved by the introduction of a special linearization of the nonlinear operator at the critical point. This linearization is a new tool even for continuous everywhere defined operators which are not necessarily Fréchet differentiable. Various cases of operators are considered: unbounded nonlinear operators with unbounded linearization, bounded nonlinear operators with bounded linearization, and operators in Hilbert spaces. Examples and counterexamples are given in 2,$"> illustrating the main results. The associated bifurcation problem for a pair of operators is also considered. The main results of the paper are substantial extensions and improvements of the classical results of Leray and Schauder (for continuous operators of Leray-Schauder type) as well as the results of Skrypnik (for bounded demicontinuous mappings of type Applications to nonlinear Dirichlet problems have appeared elsewhere.