TY - JOUR

T1 - The spectral boundary of complemented invariant subspaces in Lp(R)

AU - Buczolich, Zoltan

AU - Olevskii, Alexander

N1 - Funding Information:
Z.B. was supported by the Hungarian National Foundation for ScietnciResearch Grant no. T 016094 and FKFP B-07/1997.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33748410853&partnerID=8YFLogxK

U2 - 10.1017/S0308210500001104

DO - 10.1017/S0308210500001104

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AN - SCOPUS:33748410853

SN - 0308-2105

VL - 131

SP - 785

EP - 798

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 4

ER -