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On the boundary behaviour of functions orthogonal to invariant subspaces


Author: Kar Koi Leung
Journal: Trans. Amer. Math. Soc. 244 (1978), 67-84
MSC: Primary 30D55
DOI: https://doi.org/10.1090/S0002-9947-1978-0506610-8
MathSciNet review: 506610
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Abstract: In this paper we study the relationship between the boundary behaviour of functions in the orthogonal subspace of the invariant subspace $ \varphi {H^2}$ and the boundary behaviour of the inner function $ \varphi $ itself.


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  • [1] P. R. Ahern and D. N. Clark, On functions orthogonal to invariant subspaces, Acta Math. 124 (1970). MR 0264385 (41:8981a)
  • [2] -, Radial limits and invariant subspaces, Amer. J. Math. 92 (1970). MR 0262511 (41:7117)
  • [3] A. Beurling, On two problems concerning linear transformations in Hilbert spaces, Acta Math. 81 (1949). MR 0027954 (10:381e)
  • [4] G. T. Cargo, The radial images of Blaschke products, J. London Math. Soc. 36 (1961). MR 0133465 (24:A3296)
  • [5] -, Angular and tangential limits of Blaschke products and their successive derivatives, Canad. J. Math. 14 (1962). MR 0136743 (25:204)
  • [6] M. L. Cartwright, Integral functions, Cambridge Tract, no. 44, 1956. MR 0077622 (17:1067c)
  • [7] D. Frostman, Sur les produits de Blaschke, Kungliga Fysiografiska Sällskapets i Lund Förhandlingar, Band 12, 1942. MR 0012127 (6:262e)
  • [8] E. Hille, Introduction to general theory of reproducing kernels, Rocky Mountain J. Math. 2 (1972), 321-368. MR 0315109 (47:3658)
  • [9] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N.J., 1962. MR 0133008 (24:A2844)
  • [10] Kar-Koi Leung, Asymptotic values of modulus 1 of functions in the unit ball of $ {H^\infty }$, Trans. Amer. Math. Soc. 203 (1975), 119-128. MR 0361085 (50:13531)
  • [11] K. K. Leung and C. N. Linden, Asymptotic values of modulus 1 of Blaschke products, Trans. Amer. Math. Soc. 203 (1975), 107-118. MR 0361084 (50:13530)
  • [12] D. Protas, Tangential limits of Blaschke products and functions of bounded characteristics, Arch. Math. 22 (1972). MR 0299798 (45:8846)
  • [13] -, Tangential limits of functions orthogonal to invariant subspaces, Trans. Amer. Math. Soc. 166 (1972), 163-172. MR 0293100 (45:2179)
  • [14] -, On the accumulation of the zeros of a Blaschke product at a boundary point, Proc. Amer. Math. Soc. 34 (1972), 489-496. MR 0294645 (45:3713)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0506610-8
Keywords: $ {H^p}$ spaces, boundary behaviour, kernel functions, orthogonal invariant subspaces, Blaschke products
Article copyright: © Copyright 1978 American Mathematical Society

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