The Grassmannian/Krĕın-space approach to interpolation theory introduced in the 1980s gives a Krĕın-space geometry approach to arriving at the resolvent matrix which parametrizes the set of solutions to a NevanlinnaPick interpolation or Nehari-Takagi best-approximation problem. We review the basics of this approach and then discuss recent extensions to multivariable settings which were not anti...

Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in mani...

The aim of this paper is to obtain new coincidence and common fixed point theorems by using Lipschitz type conditions of hybrid maps (not necessarily continuous) on a metric space. As applications, we demonstrate the existence of common fixed points from the set of best approximations. Our work sets analogues, unifies and improves various known results existing in the literature. 2000 Mathemati...

In this work, we first introduce the concept of approximate sequence and establish some new convergence theorems for approximate sequences. By applying our new convergence theorems, we obtain new best proximity point theorems which improve and generalize some known results in the literature. As applications, some simultaneous generalizations of common fixed point theorems of Banach type, Kannan...

By the use of the transfer formula, the methods of weight functions and technique of Real Analysis, a multidimensional Hilbert-type integral inequality with a few parameters and a best possible constant factor related to the kernel of logarithm function is given. The equivalent forms and some reverses are obtained. The operator expressions and a few particular results related to the kernels of ...

We consider nonparametric estimation of a multivariate function and its partial derivatives at a fixed point when the Riesz transform of the function is observed in Gaussian white noise. We assume that the unknown function belongs to some Sobolev class and construct an estimation procedure which achieves the best asymptotic minimax risk when the smoothness of the function is unknown. Mathematic...

The paper is concerned with best constants in Markov-type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself. The norm of the polynomial is taken in L2 with the Gegenbauer weight corresponding to a parameter α , while the derivative is measured in L2 with the Gegenbauer weight for a parameter β . Under the assumption that β −α is an intege...

In the present paper, we study the cuspidalization problem for fundamental groups of configuration spaces of proper hyperbolic curves over finite fields. The goal of this paper is to show that any Frobenius-preserving isomorphism between the geometrically pro-l fundamental groups of hyperbolic curves induces an isomorphism between the geometrically pro-l fundamental groups of the associated con...

Correspondence: penggao@ntu. edu.sg Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore Abstract We present some results concerning the l norms of weighted mean matrices. These results can be regarded as analogues to a result of Bennett concerning weighted Carleman’s inequalities. 2000 Mathematics Subject Classifica...