The spectral boundary of complemented invariant subspaces in Lp(R)

Zoltan Buczolich, Alexander Olevskii

Research output: Contribution to journalArticlepeer-review


In this paper we construct a compact set K of zero Hausdorff dimension that satisfies certain ‘arithmetic-type’ thickness properties. The concept of ‘arithmetic thickness’ has its origins in applications to harmonic analysis, introduced in a paper by Lebedev and Olevskii. For example, there are no spectral sets whose ‘essential boundary’ can contain the above set K.

Original languageEnglish
Pages (from-to)785-798
Number of pages14
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number4
StatePublished - 2001


FundersFunder number
Hungarian National Foundation for ScietnciResearch


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