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Steklov Institute of Mathematics at St.Petersburg

#
PREPRINT 15/2002

M. M. SKRIGANOV
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HARMONIC ANALYSIS ON TOTALLY
DISCONNECTED GROUPS AND IRREGULARITIES
OF POINT DISTRIBUTIONS

This preprint was accepted August 15, 2002

Contact:
` M. M. Skriganov `

ABSTRACT:
The goal of this paper is to study point distributions
in the multi-dimensional unit cube which possess the structure
of finite abelian groups with respect to certain $p$-ary
arithmetic operations. Such distributions can be thought
of as finite subgroups in a compact totally disconnected group
of the Cantor type. We apply the methods of $L^q$ harmonic
analysis to estimate very precisely the $L^q$-discrepancies for
such distributions. Following this approach, we explicitly
construct point distributions with the minimal order of the
$L^q$-discrepancy for each $q, $1\le q\le \infty$.

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