Asymptotic values of modulus $1$ of Blaschke products
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- by K. K. Leung and C. N. Linden PDF
- Trans. Amer. Math. Soc. 203 (1975), 107-118 Request permission
Abstract:
A sufficient condition is found for each subproduct of a Blaschke product to have an asymptotic value of modulus 1 along a prescribed arc of a specified type in the unit disc. The condition obtained is found to be necessary in the case of further restrictions of the arc, and the two results give rise to a necessary and sufficient condition for the existence of ${T_\gamma }$-limits of modulus 1 for Blaschke products.References
- G. T. Cargo, Angular and tangential limits of Blaschke products and their successive derivatives, Canadian J. Math. 14 (1962), 334–348. MR 136743, DOI 10.4153/CJM-1962-026-2
- Otto Frostman, Sur les produits de Blaschke, Kungl. Fysiografiska Sällskapets i Lund Förhandlingar [Proc. Roy. Physiog. Soc. Lund] 12 (1942), no. 15, 169–182 (French). MR 12127
- G. M. Golusin, Geometrische Funktionentheorie, HochschulbĂĽcher fĂĽr Mathematik, Band 31, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957 (German). MR 0089896
- C. N. Linden and H. Somadasa, On tangential limits of Blaschke products, Arch. Math. (Basel) 18 (1967), 416–424. MR 233985, DOI 10.1007/BF01898836
- David Protas, Tangential limits of Blaschke products and functions of bounded characteristic, Arch. Math. (Basel) 22 (1971), 631–641. MR 299798, DOI 10.1007/BF01222628
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 203 (1975), 107-118
- MSC: Primary 30A72; Secondary 30A76
- DOI: https://doi.org/10.1090/S0002-9947-1975-0361084-2
- MathSciNet review: 0361084