On the rigidity part of Schwarz Lemma

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Akyel T., Örnek B. N.

3rd International Conference of Mathematical Sciences, ICMS 2019, İstanbul, Türkiye, 4 - 08 Eylül 2019, cilt.2183, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2183
  • Doi Numarası: 10.1063/1.5136123
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: Bilogarithmic concave majorant, Harnack inequality, Holomorphic function, Phragmen-Lindelof princible
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Maltepe Üniversitesi Adresli: Evet

Özet

We consider the rigidity part of Schwarz Lemma. Let f be a holomorphic function in the unit disc D and |Rf(z)| <1 for |z| < 1. We generalize the rigidity of holomorphic function and provide sufficient conditions on the local behaviour of f near a finite set of boundary points that needs f to be a finite Blaschke product. For a different version of the rigidity theorems of D. Burns-S. Krantz and D. Chelst, we present some more general results in which the bilogaritmic concave majorants are used. The strategy of these results relies on a special version of Phragmen-Lindelöf princible and Harnack inequality.