Asymptotic values of modulus 1 of functions in the unit ball of 𝐻^{∞}

Leung, Kar Koi

doi:10.1090/S0002-9947-1975-0361085-4

Asymptotic values of modulus $1$ of functions in the unit ball of $H^{\infty }$
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Trans. Amer. Math. Soc. 203 (1975), 119-128 Request permission

Abstract:

The main purpose of this paper is to prove a theorem concerning a necessary and sufficient condition for an inner function to have a limiting value of modulus 1 along an arc inside the unit disc, terminating at a point of the unit circle.

References

P. R. Ahern and D. N. Clark, Radial $n\textrm {th}$ derivatives of Blaschke products, Math. Scand. 28 (1971), 189–201. MR 318495, DOI 10.7146/math.scand.a-11015

Funktionentheorie

Theory of functions of a complex variable

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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
E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999, DOI 10.1017/CBO9780511566134
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
K. K. Leung and C. N. Linden, Asymptotic values of modulus $1$ of Blaschke products, Trans. Amer. Math. Soc. 203 (1975), 107–118. MR 361084, DOI 10.1090/S0002-9947-1975-0361084-2
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
E. C. Titchmarsh, Han-shu lun, Science Press, Peking, 1964 (Chinese). Translated from the English by Wu Chin. MR 0197687