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Literature cited
N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in a Hilbert Space [in Russian], Nauka, Moscow (1966).
I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow-Leningrad (1950).
K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, New Jersey (1962).
B. Sz. -Nagy and C. Foias, Harmonic Analysis of Operators in a Hilbert Space [Russian transltion], Mir, Moscow (1970).
H. Helson, Lectures on Invariant Subspaces, Academic Press, New York (1964).
G. K. Rota, “Note on the invariant subspaces of linear operators,” Rend Circ. Mat. Palermo,8, No. 2, 182–185 (1959).
P. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton (1967).
P. Lax and R. Phillips, Scattering Theory, Academic Press, New York-London (1967).
A. I. Plesner, “On semiunitary operators,” Dokl. Akad. Nauk SSSR,25, 708–710 (1939).
Yu. A. Rozanov, Stationary Random Processes [in Russian], Fizmatgiz, Moscow (1963).
Literature cited
A. Beurling, “On two problems concerning linear transformations in Hilbert space,” Acta Math.,81, Nos. 1–2, 239–255 (1949).
B. Moore, III, “The Szegö infimum,” Proc. Am Math. Soc.,29, No. 1, 55–62 (1971).
K. Urbanik, “Szegö's theorem for Orlicz spaces,” Bull. Acad. Polon. Sci. Ser. Math. Phys. Astorn.,14, No. 9, 503–509 (1966).
Literature cited
R. G. Douglas, H. S. Shapiro, and A. L. Shields, “Cyclic vectors and invariant subspaces for the Backward shift operator,” Ann. Inst. Fourier,20, No. 1, 37–76 (1970).
L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).
A. A. Gonchar, “On generalized analytic continuation,” Mat. Sb.,76 (118), No. 1, 135–146 (1968).
Literature cited
D. Sarason, “Weak-star density of polynomials,” J. Reine und Angew. Math.,252, 1–15 (1972).
A. I. Plesner, “Functions of a maximal operator,” Dokl. Akad. Nauk SSSR,23, 327–330 (1939).
Literature cited
I. Ts. Gokhberg and M. G. Krein, The Theory of Volterra Operators in as Hilbert Space and its Applicatioins [in Russian], Nauka, Moscow (1967).
M. S. Brodskii, Triangular and Jordan Representations of Linear Operators [in Russian], Nauka, Moscow (1969).
D. Sarason, “A remark on the Volterra operator,” J. Math. Anal. Appl.,12, 244–246 (1965).
B. Sz. -Nagy and C. Foias, “Sur les contractions de l'espace de Hilbert, VII, Triangulation canoniques, Fonction minimum,” Acta Sci. Math.,25, Nos. 1–2, 12–37 (1964).
D. Sarason, “Generalized interpolation in H∞,” Trans. Am. Math. Soc.,127, No. 2 179–203
N. Rushfield, “Inner factors and Blaschke products,” Proc. Am. Math. Soc.,17, No. 3, 572–579 (1966).
N. K. Nikol'skii, “Five problems on invariant subspaces,” Zap. Nauchn. Semin. LOMI (Leningrad),23, 115–127 (1971).
J.-P. Kahane and R. Salem, Ensemble Parfaites et series Trigonometrique, Paris (1963).
N. K. Nikol'skii, “A criterion for weak invertibility in spaces of analytic functions distinguished By growth bounds,” Zap. Nauchn, Semin. LOMI (Leningrad),30, 106–129 (1972).
D. Sarason, “Weak-star density of polynomials,” J. Reine and Angew, Math.,252, 1–15 (1972).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 39, pp. 59–93, 1974.
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Nikol'skii, N.K. Lectures on the shift operator. J Math Sci 8, 41–65 (1977). https://doi.org/10.1007/BF01455323
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DOI: https://doi.org/10.1007/BF01455323