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Invariant subspaces of Hardy classes on infinitely connected plane domains. (English) Zbl 0266.46040


MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
30D55 \(H^p\)-classes (MSC2000)
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References:

[1] Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 17. · Zbl 0033.37701
[2] R. Buck, Algebraic properties of classes of analytic functions, Seminars on Analytic Functions, vol. 2, Princeton, N. J., 1957, 175-188.
[3] Morisuke Hasumi, Invariant subspace theorems for finite Riemann surfaces, Canad. J. Math. 18 (1966), 240 – 255. · Zbl 0172.41603
[4] Morisuke Hasumi and T. P. Srinivasan, Doubly invariant subspaces. II, Pacific J. Math. 14 (1964), 525 – 535. · Zbl 0136.11001
[5] Maurice Heins, Hardy classes on Riemann surfaces, Lecture Notes in Mathematics, No. 98, Springer-Verlag, Berlin-New York, 1969. · Zbl 0176.03001
[6] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. · Zbl 0734.46033
[7] C. Kennel, Locally outer functions (to appear). · Zbl 0363.30041
[8] M. Parreau, Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier Grenoble 3 (1951), 103 – 197 (1952) (French). · Zbl 0047.32004
[9] Arthur H. Read, A converse of Cauchy’s theorem and applications to extremal problems., Acta Math. 100 (1958), 1 – 22. · Zbl 0142.04503
[10] L. A. Rubel and A. L. Shields, The space of bounded analytic functions on a region, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 235 – 277. · Zbl 0152.13202
[11] L. A. Rubel and A. L. Shields, The second duals of certain spaces of analytic functions, J. Austral. Math. Soc. 11 (1970), 276 – 280. · Zbl 0197.39001
[12] Walter Rudin, Essential boundary points, Bull. Amer. Math. Soc. 70 (1964), 321 – 324. · Zbl 0133.03605
[13] Michael Voichick, Ideals and invariant subspaces of analytic functions, Trans. Amer. Math. Soc. 111 (1964), 493 – 512. · Zbl 0147.11502
[14] Michael Voichick, Extreme points of bounded analytic functions on infinitely connected regions, Proc. Amer. Math. Soc. 17 (1966), 1366 – 1369. · Zbl 0154.32902
[15] Harold Widom, The maximum principle for multiple-valued analytic functions, Acta Math. 126 (1971), 63 – 82. · Zbl 0203.38302
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