摘要:

LetGbe a compact body of positive volume inRn, star‐shaped with respect to an interior point, taken to be the origin. For subsets Ω ofRn, the functionalIL(G,Ω)=Vol(G) suplatticesΛs{detΛ:Ω⊆Λ+G}represents the minimum density with which Ω can be covered by a lattice ∧ of translates ofG. We obtain an upper bound onIL(G, Zn).If the attributes ofGare supplemented with convexity, writeHinstead. We also bound abovem(r,f′/f)=12π∫02πlog+|f′(ret0)/f(ret0)|dθthe classicalminimum lattice‐covering densityofH. No symmetry conditions are imposed onGandH.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.193

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.201

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.215

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In [10] various conjectural identities between the ranks and the cranks of partitions modulo 8, 9 and 12 were proposed. These conjectures have now all been proved [14,15,11], with three exceptions. Here, we prove these three exceptions. Methods similar to those used here may be used to establish all the theorems and conjectures of [10].

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.222

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

The purpose of this paper is to give necessary and sufficient conditions for the boundedness fromLvp(R+) toLuqof Volterra convolution operators of the formkf(x)=∫0xk(x−y)f(y)dy, wherek(x)is a non‐negative non‐decreasing kernel satisfyingk(x+y)⩽D(k(x)+k(y)) for allx, yɛR+. The cases of 1

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.232

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Letfbe meromorphic in {z:|z|

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.243

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. A number of classical inequalities holding for polynomials can be extended for generalized polynomials utilizing the generalized degree in place of the ordinary one. Remez established a sharp upper bound for the maximum modulus on [− 1,1] of algebraic polynomials of degree at mostnif the measure of the subset of [− 1,1], where the modulus of the polynomial is at most 1, is known. In this paper a numerical version of the Remez inequality is extended for generalized complex algebraic polynomials and its trigonometric and pointwise algebraic analogues are discussed. The results are new even for ordinary polynomials.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.255

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.265

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.279

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this paper we answer a question of Wilken by constructing an example of a non‐trivial, strongly regular uniform algebra on a compact, Hausdorff; topological space. We also show how to obtain an example on a compact metric space, and we give examples both with and without the property that every point is a peak point.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.2.288

出版商:Oxford University Press    

年代:2016

数据来源: WILEY