摘要:

We show that there is a degree a REA in and low over0′ such that no minimal degree below0′ jumps to a degree above a. We also show that every nonlow recursively enumerable degree bounds a nonlow minimal degree.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.417

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

This paper examines the limit points of continuous Z‐cocycles defined on a minimal dynamical system and taking values in an abelian metrisable group.This is motivated by and applied to the study of classical exponential seriesΣn=1Ne2πi(n2θ+nx)to show, in particular, that if θ is a transcendental number with lim infqq3/2‖qθ‖<∞, then for eachxchosen from a denseGδsubset of [0, 1], these partial sums are dense in C. Indeed the associated cocycle is topologically transitive. Several generalisations to higher degree polynomials and higher dimensions are presented.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.440

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Ladder determinantal rings are rings associated with ideals of minors of certain subsets of a generic matrix of indeterminates. By results of Abhyankar, Narasimhan, Herzog and Trung, and Conca, they are known to be Cohen‐Macaulay normal domains. In this paper we characterize the Gorenstein property of ladder determinantal rings in terms of the shape of the ladder.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.453

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this paper we investigate the left cell representations of the Iwahori‐Hecke algebras associated to a finite Coxeter groupW. Our main result shows thatTw0, wherew0is the element of longest length inW, acts essentially as an involution upon the canonical bases of a cell representation. We describe some properties of this involution, use it to further describe the left cells, and finally show how to realize each cell representation as a submodule of ℋ. Our results rely upon certain positivity properties of the structure constants of the Kazhdan‐Lusztig bases of the Hecke algebra and so have not yet been shown to apply to all finite Coxeter groups.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.475

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.489

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

This paper characterizes the boundedness of certain bilinear forms on Dirichlet type spaces. The main tool is the Littlewood‐Paley theory. Applications to the preduals of the related function spaces including BMO and Bloch spaces, and the boundedness of certain commutators are also indicated.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.498

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.515

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.530

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We consider questions of rational and polynomial approximation, and related extension questions, for various normed spaces of infinitely differentiable functions on perfect compact subsets of the complex plane C and the real line R. We obtain an approximation theorem for compact planar sets which are, in a precise sense, locally radially self‐absorbing. All smoothly‐bounded compact sets are of this type. We give a variety of results and counterexamples on extension, mainly in the one‐dimensional case. We also prove polynomial approximation theorems for totally‐disconnected sets, linear sets, and some others.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.541

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We give a new short proof of H. Landau's density result on necessary conditions for the sampling and interpolation of certain entire functions in the case that the boundary of the spectrum has measure 0. For the proof we adapt a method that has been recently developed by J. Ramanathan and T. Steger in the context of time‐frequency analysis. As a consequence of a general theorem for the comparison of densities we obtain several new results about the density of irregular sampling of band‐limited functions with derivatives and differential operators.

ISSN:0024-6107    

DOI:10.1112/jlms/54.3.557

出版商:Oxford University Press    

年代:2016

数据来源: WILEY