This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue of some other quasisymmetric automorphism σ is given.
@article{bwmeta1.element.bwnjournal-article-bcpv31z1p303bwm,
author = {Partyka, Dariusz},
title = {The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle},
journal = {Banach Center Publications},
volume = {31},
year = {1995},
pages = {303-310},
zbl = {0833.30012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p303bwm}
}
Partyka, Dariusz. The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle. Banach Center Publications, Tome 31 (1995) pp. 303-310. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p303bwm/
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