The Library
Pair correlations of sequences in higher dimensions
Tools
Nair, R and Pollicott, Mark. (2007) Pair correlations of sequences in higher dimensions. Israel Journal of Mathematics, Volume 157 (Number 1). pp. 219238. ISSN 00212172
Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s118560060009z
Abstract
We consider a system of "generalised linear forms" defined on a subset x = (x(ij)) of Rd by
L1 (x) (k) = d(1) g(1j)(k) (x(1j)), ...Ll (x) (k) = d(l) g(lj)(k) (xlj) is an element of R, for k >= 1,
where d = d(1) + ...+ d(l) and for each pair of integers (i, j), 1 <= i <= l l <= j <= d(i) the sequence of functions (g(ij)(k)(x))(kappa=1)(infinity) is differentiable on an interval Xij. Then let
XK(x) = ({L1(x)(k)}, . . . , {Ll(x)(k)}) is an element of Tl
for x in the Cartesin product X = x(i=1)(l) x (di)(j = 1) Xij subset of Rd. Let R = I1 x . . . x Il be a rectangle in Tl and for each N >= 1 let
VN(R) = Sigma(1 <= n not equal m <= N) XR(Xn)(X)(Xm)(x))
and then define
Delta(N) = sup {VN (R)  N (N1) leb (R) } R subset of Tl
where the supremum is over all rectangles in Tl. We show that for almost every x is an element of Td we have that
Delta(N) = O(N(log N)(alpha))
for appropiate alpha. Other related results are also described.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Journal or Publication Title:  Israel Journal of Mathematics  
Publisher:  Magnes Press  
ISSN:  00212172  
Official Date:  January 2007  
Dates: 


Volume:  Volume 157  
Number:  Number 1  
Number of Pages:  20  
Page Range:  pp. 219238  
Identifier:  10.1007/s118560060009z  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
URI:  http://wrap.warwick.ac.uk/id/eprint/31717 
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Actions (login required)
View Item 