On the boundary behaviour of functions orthogonal to invariant subspaces

Leung, Kar Koi

doi:10.1090/S0002-9947-1978-0506610-8

On the boundary behaviour of functions orthogonal to invariant subspaces
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by Kar Koi Leung

Trans. Amer. Math. Soc. 244 (1978), 67-84

DOI: https://doi.org/10.1090/S0002-9947-1978-0506610-8

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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.

References

P. R. Ahern and D. N. Clark, On functions orthogonal to invariant subspaces, Acta Math. 124 (1970), 191–204. MR 264385, DOI 10.1007/BF02394571
P. R. Ahern and D. N. Clark, Radial limits and invariant subspaces, Amer. J. Math. 92 (1970), 332–342. MR 262511, DOI 10.2307/2373326
Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019
G. T. Cargo, The radial images of Blaschke products, J. London Math. Soc. 36 (1961), 424–430. MR 133465, DOI 10.1112/jlms/s1-36.1.424
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
M. L. Cartwright, Integral functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 44, Cambridge, at the University Press, 1956. MR 0077622
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
Einar Hille, Introduction to general theory of reproducing kernels, Rocky Mountain J. Math. 2 (1972), no. 3, 321–368. MR 315109, DOI 10.1216/RMJ-1972-2-3-321
Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
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 361085, DOI 10.1090/S0002-9947-1975-0361085-4
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
David Protas, Tangential limits of functions orthogonal to invariant subspaces, Trans. Amer. Math. Soc. 166 (1972), 163–172. MR 293100, DOI 10.1090/S0002-9947-1972-0293100-8
David Protas, On the accumulation of the zeros of a Blaschke product at a boundary point, Proc. Amer. Math. Soc. 34 (1972), 489–496. MR 294645, DOI 10.1090/S0002-9939-1972-0294645-2