The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle

• Autorzy: Dariusz Partyka
• Języki publikacji: EN

Abstrakty

EN

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 $A_γ:ℍ → ℍ$ 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.

Słowa kluczowe

EN

quasisymmetric automorphisms; harmonic conjugation operator; quasiconformal mappings; eigenvalues and spectral values of a linear operator; Teichmüller mappings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 31
• Numer: 1
• Strony: 303-310

Daty

wydano

1995

Twórcy

autor

Dariusz Partyka

• Department of Mathematics, Maria Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

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