Wann sind die Grunskyschen Koeffizientenbedingungen hinreichend fürQ-quasikonforme Fortsetzbarkeit?

Kühnau, Reiner

doi:10.1007/bf02621917

Cited by 54 publications

(35 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This completes the proof. R e m a r k. This result seems to be closely related to that in [Kü,p. 302].…”

Section: Main Results and Proofssupporting

confidence: 69%

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

Partyka¹

1995

Banach Center Publ.

View full text Add to dashboard Cite

Abstract. 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 ∆. In particular, the norm of the generalized harmonic conjugation operator Aγ : 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.

show abstract

“…This completes the proof. R e m a r k. This result seems to be closely related to that in [Kü,p. 302].…”

Section: Main Results and Proofssupporting

confidence: 69%

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

Partyka¹

1995

Banach Center Publ.

View full text Add to dashboard Cite

show abstract

“…By [24,Theorem 4.4.2], the set Λ * (Γ) of all eigenvalues of a quasicircle Γ ⊂ C coincides with the set Λ * γ , where γ is a welding homeomorphism of Γ. Therefore, Theorem 3.1 is closely related to various results involving these constants obtained by Kühnau ([15], [16], [17]), Schiffer ([29]) and Krushkal ([6], [7], [8,Sect. 2]); see also the survey article by Krushkal [9, p. 528] and the references given there.…”

Section: Remark 33mentioning

confidence: 80%

“…e.g. [17]. Having disposed of the equalities (0.3), Krzyż proposed to modify them by using the continuous mappings H : cl(D) → cl(Ω) and H * : cl(D * ) → cl(Ω * ) which are conformal in the unit disk D := {z ∈ C : |z| < 1} and in D * := {z ∈ C : |z| > 1} ∪ {∞}, respectively.…”

Section: Introductionmentioning

confidence: 99%