Composition operators with maximal norm on weighted Bergman spaces

We prove that any composition operator with maximal norm on one of the weighted Bergman spaces (in particular, on the space ) is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space , where every inner function induces a composition operator with maximal norm.

     

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications.     

一类奇异非线性两点边值问题的 Galerkin 解的误差估计

本文对一类奇异两点边值问题采用了对称的Galerkin方法.通过利用Green函数,对线性问题得到了拟最优的最大范数误差估计并将这一结果推广到了非线性问题.本文最后列举了一些数值试验结果,这些结果很好地验证了理论结果.     

Operator martingale decompositions and the Radon-Nikodým property in Banach spaces

We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon-Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney-Schaefer l-tensor product , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon-Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on . Secondly, we derive a Riesz decomposition for uniform amarts of maps acting between a Banach lattice and a Banach space. This result is used to characterize Banach spaces with the Radon-Nikodým property in terms of uniformly norm bounded uniform amarts of maps that are norm convergent. In the case 1<p<∞, our results yield Lp(μ,Y)-space analogues of some of the well-known results on uniform amarts in L¹(μ,Y)-spaces.     

Improved Young and Heinz inequalities for matrices

We give refinements of the classical Young inequality for positive real numbers and we use these refinements to establish improved Young and Heinz inequalities for matrices.     

Rough singular integrals supported on submanifolds

In this paper, the authors study the boundedness of the singular integral operators associated to submanifolds on Triebel-Lizorkin spaces and Besov spaces. Moreover, the authors also establish an lq-valued inequality for the maximal operators associated to submanifolds in this paper.     

Uniform convergence and integrability of Fourier integrals

Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on Lp-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions.     

Lattice based extended formulations for integer linear equality systems

We study different extended formulations for the set with in order to tackle the feasibility problem for the set Pursuing the work of Aardal, Lenstra et al. using the reformulation , our aim is to derive reformulations of the form with 0  ≤  s ≤ n − m where preferably all the coefficients of P are small compared to the coefficients of A and T. In such cases the new variables μ appear to be good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. We give a polynomial time algorithm for identifying such P, T if possible, and for the case that A has one row a we analyze the reformulation when s = 1, that is, one μ-variable is introduced. In particular, we determine the integer width of the extended formulations in the direction of the μ-variable, and derive a lower bound on the Frobenius number of a. We conclude with some preliminary tests to see if the reformulations are effective when the number s of additional constraints and variables is limited. This work was partly carried out within the framework of ADONET, a European network in Algorithmic Discrete Optimization, contract no. MRTN-CT-2003-504438. The first author is financed in part by the Dutch BSIK/BRICKS project. The research was carried out in part while the second author visited CWI, Amsterdam with the support of the NWO visitor grant number B 61-556.     

Random martingales and localization of maximal inequalities

Let (X,d,μ) be a metric measure space. For ∅≠R⊆(0,∞) consider the Hardy-Littlewood maximal operator