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A Metric Discrepancy Estimate in Higher Dimensions Using L^2 Methods

Hailiza Kamarul Haili, (2001) A Metric Discrepancy Estimate in Higher Dimensions Using L^2 Methods. Bulletin of the Malaysian Mathematical Sciences Society, 24 (1). pp. 59-67. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v24n1/v24n1p7.pdf

Affiliations

Universiti Sains Malaysia, School of Mathematical Sciences

Abstract

We prove a general metrical result, which contains as a special case a discrepancy estimate, related to the uniform distribution of expressions of the form $ ( \lambda_{1,i,n} x_{1,i} + \cdots + \lambda_{k(i),i,n} x_{k(i)} )_{n=1}^\infty (i=1, \cdots ,d; 1 \leq j \leq k(i)) $ for Lebesgue almost all points in $ X = X_1 \times \cdots \times X_d $ with $ X_i = [a_{1,i} , b_{1,i}] \times \cdots \times [a_{k(i),i} , b_{k(i),i}] $ where for each pair $ j,i $ there exist $c_{j,i} > 0$ such that $ | \lambda_{j,i,(n+1)} - \lambda_{j,i,n} | \geq c_{j,i} $.

Item Type:Journal
Subjects:Q Science, Computer Science
ID Code:1330

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