Kathryn E. Hare

Interpolation and Sidon sets for compact groups

Preface .- Introduction .- Hadamard Sets.-

Sums of Cantor sets

\epsilon

CLASSIFYING CANTOR SETS BY THEIR FRACTAL DIMENSIONS

-Kronecker sets.- Sidon sets: Introduction and decomposition properties.- Characterizations of

Sums of Cantor sets yielding an interval

I_0

I0 SETS FOR COMPACT, CONNECTED GROUPS: INTERPOLATION WITH MEASURES THAT ARE NONNEGATIVE OR OF SMALL SUPPORT

sets.- Proportional characterizations of Sidon sets.- Decompositions of

The independence of characters on non-abelian groups

I_0

A structural criterion for the existence of infinite central Λ(p) sets

sets.- Sizes of thin sets.- Sets of zero discrete harmonic density.- Related results.-Open problems.- Appendices (Groups, Probability, Combinatoric results,...).- Bibliography.- Author index.- Subject index.- Index of notation.

CENTRAL INTERPOLATION SETS FOR COMPACT GROUPS AND HYPERGROUPS

We find conditions on the ratios of dissection of a Cantor set so that the group it generates under addition has positive Lebesgue measure. In particular, we answer affirmatively a special case of a conjecture posed by J. Palis.

A Fourier series formula for energy of measures with applications to Riesz products

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their -Hausdorff and -packing measures, for the family of dimension functions , and characterize this classification in terms of the underlying sequences.

Maximal Operators and Cantor Sets

In this paper we prove that if a Cantor set has ratios of dissection bounded away from zero, then there is a natural number N, such that its N-fold sum is an interval. Moreover, for each element z of this interval, we explicitly construct the N elements of C whose sum yields z. We also extend a result of Mendes and Oliveira showing that when s is irrational Ca + Ca* is an interval if and only ifa/(l— 2a)a /(\ — 2a) > 1. 2000 Mathematics subject classification: primary 28A80, 26A30.