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911.
The context of much of the work in this paper is that of a backward-shift invariant subspace of the form , where B is some infinite Blaschke product. We address (but do not fully answer) the question: For which B can one find a (convergent) sequence in KB such that the sequence of real measures converges weak-star to some nontrivial singular measure on ? We show that, in order for this to hold, KB must contain functions with nontrivial singular inner factors. And in a rather special setting, we show that this is also sufficient. Much of the paper is devoted to finding conditions (on B) that guarantee that KB has no functions with nontrivial singular inner factors. Our primary result in this direction is based on the “geometry” of the zero set of B. 相似文献
912.
Our purpose in the paper is to find the most general linear congruence relation of the Hardy-Williams type for linear combinations of special values of Kubota-Leopoldt 2-adic L-functions L2(k,χω1−k) with k running over any finite subset of not necessarily consisting of consecutive integers (see Acta Arith. 47 (1986) 263; Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, 1995/1996; Publ. Math. Debrecen 56 (2000) 677 and cf. Mathematics and Its Applications, Vol. 511, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000). If k runs over finite subsets of consisting of consecutive integers see Compositio Math. 111 (1998) 289; Publ. Math. Debrecen 56 (2000) 677; Hardy and Williams, 1986; Compositio Math. 75 (1990) 271; Acta Arith. 71 (1995) 273; 52 (1989) 147; J. Number Theory 34 (1990) 362. In order to obtain the most general congruences of this type we make use of divisibility properties of the generalized Vandermonde determinants obtained in Spie? et al. (Divisibility properties of generalized Vandermonde and Cauchy determinants, Preprint 627, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 2002). This allows us to simplify our main Theorem 2 and obtain Theorem 3 where the most general form of the linear congruence relation is given. 相似文献
913.
We investigate the distribution of the numbers x∈[1,p] for which all lie in a subset of the set of multiplicative inverses modulo a prime p. Here the ai are integers coprime to p and the numbers are distinct . 相似文献
914.
915.
Alexander Goldenshluger 《Journal of multivariate analysis》2003,84(1):40-60
The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is asymptotically minimax over ellipsoids in ?2. The method is based on a regularized least squares estimator with weights of the Pinsker filter. We also consider the case of dynamic linear regression, which is important in the context of transfer function modeling. 相似文献
916.
Alexandr V. Kostochka 《Combinatorica》2002,22(2):275-285
Dedicated to the memory of Paul Erdős
Let f(r,p,t) (p > t >= 1, r >= 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f(r,p,2) for p = 3, 4, 5, 6 were found in [1] and bounds on f(r,7,2) are given in [3]. Here we prove that for large p and huge r.
Received September 23, 1999
RID="*"
ID="*" This work was partially supported by the grant 99-01-00581 of the Russian Foundation for Fundamental Research and the
Dutch–Russian Grant NWO-047-008-006. 相似文献
917.
Gerald Beer 《Monatshefte für Mathematik》2000,129(4):267-280
By a metric mode of convergence to infinity in a regular Hausdorff space X, we mean a sequence of closed subsets of X with and , and a sequence (or net) in X is convergent to infinity with respect to provided for each contains eventually. Modulo a natural equivalence relation, these correspond to one-point extensions of the space with a countable
base at the ideal point, and in the metrizable setting, they correspond to metric boundedness structures for the space. In
this article, we study the interplay between these objects and certain continuous functions that may determine the metric
mode of convergence to infinity, called forcing functions. Falling out of our results is a simple proof that each noncompact
metrizable space admits uncountably many distinct metric uniformities.
(Received 2 March 1999) 相似文献
918.
Haruhisa Nakajima 《manuscripta mathematica》2000,102(2):139-158
In order to inquire into invariants of non-semisimple groups, we introduce and study relative versions of equidimensionality
and stabilty, which are called relative quasi-equidimensionality and relative stability, of actions of affine algebraic groups,
especially of reductive groups, on affine varieties. As an application of our results, for complex reductive groups of semisimple
rank one, we characterize, respectively, relatively stable representations and relatively equidimensional representations
and, consequently, show that every equidimensional representation is cofree.
Received: 23 October 1998 相似文献
919.
A structure theorem is proved for a finitely generated group with a finitely generated virtually polycyclic codimension one
subgroup.
Oblatum 12-II-1999 & 18-XI-1999?Published online: 21 February 2000 相似文献
920.
Abstract
Let A be a unital simple C*-algebra of real zero, stable rank one, with weakly unperforated K
0(
A) and unique normalized quasi-trace τ, and let X be a compact metric space. We show that two monomorphisms φ, ψ : C(X)→A are approximately unitarily equivalent if and only if φ and ψ induce the same element in KL(C(X), A) and the two lineal functionals τ∘φ and τ∘ψ are equal. We also show that, with an injectivity condition, an almost multiplicative
morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism.
Research partially supported by NSF Grants DMS 93-01082 (H.L) and DMS-9401515(G.G). This work was reported by the first named
author at West Coast Operator Algebras Seminar (Sept. 1995, Eugene, Oregon) 相似文献