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Literature Cited
J. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).
P. Koosis, Introduction to Hp Spaces, Cambridge University Press, New York (1980).
K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, NJ (1962).
S. M. Nikol'skii, Treatise on Shift Operators, Springer-Verlag, New York (1986).
A. B. Aleksandrov, “Invariant subspaces for the backward shift operator in the space HP (p ∈ (0, 1)),” Zap. Nauchnl Sem. Leningrad. Otdel. Mat. Inst. Stteklov (LOMI),92, 7–29 (1979).
G. Ts. Tumarkin, “Description of a class of functions admitting the approximation by fractions with preassigned poles,” Izv. Akad. Nauk Armyan. SSR, Ser. Math.,1, No. 2, 89–105 (1966).
R. G. Douglas, H. S. Shapiro, and A. L. Shields, “Cyclic vectors and invariant subspaces for the backward shift operator,” Ann. Inst. Fourier (Grenoble),20, No. 1, 37–76 (1970).
W. Cohn, “Carleson measures for functions orthogonal to invariant subspaces” Pac. J. Math.,103, No. 2, 367–384 (1982).
A. L. Vol'berg, “Thin and thick families of rational functions” Lect. Notes Math.,864, 440–480 (1981).
B. Jöricke and V. P. Khavin, “Traces of harmonic functions and comparison of Lp-norms of analytic functions,” Math. Nachr.,123, 225–254 (1985).
S. R. Treil' and A. L. Vol'berg, “Embedding theorems for invariant subspaces of the inverse shift operator,” Zap. Nauchn Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI),149, 38–51 (1986).
K. M. D'yakonov, “An interpolation problem and equivalent norms in the spaces Kθ p,” Vestn. Leningr. Univ.,1, No. 4, 104–105 (1988).
K. M. D'yakonov, “The geometry of the unit ball in the space Kθ 1,” Geometric problems of the theory of functions and sets, 52–54 (1987).
M. V. Klibanov, “Determination of a function of a compact support from the modulus of its Fourier transform, and the inverse scattering problem,” Differents. Uravn.,22, No. 10, 1790–1798 (1986).
S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, New York (1975).
V. N. Logvinenko and Yu. F. Sereda, “Equivalent norms in spaces of entire functions of exponential type,” Teor. Funkcii, Funkcional. Anal. Prilozhen., No. 20, 62–78 (1973).
L. I. Ronkin, “Entire functions,” Itogi Nauki i Tekhniki, VINITI. Sovremennye Problemy Matematiki,9, 5–36 (1986).
L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, New York (1983).
E. C. Titchmarsh, The Theory of Functions, 2nd ed., University Press, London (1975).
E. M. Tchirki (ed.), “Some unsolved problems in the multidimensional complex analysis,” Preprint Akad. Nauk SSR, Sib. Otd., Institut Fiz., Krasnoyarsk (1987).
M. G. Krein and A. A. Nudel'man, “A representation of entire functions that are positive on the real axis, on the halfaxis, or outside a finite interval,” Mat. Issled.,61, 40–59 (1981).
T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N. J. (1969).
K. Yoshida, Functional Analysis, 6th ed., Springer-Verlag, Berlin-New York (1980).
S. V. Kislyakov, “Classical problems of Fourier analysis” Itogi Nauki i Tekhniki, VINITI. Sov. Probl. Mat.,15, 135–196 (1987).
Additional information
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 6, pp. 64–79, November–December, 1990.
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D'yakonov, K.M. Moduli and arguments of analytic functions from subspaces of Hp that are invariant for the backward shift operator. Sib Math J 31, 926–939 (1990). https://doi.org/10.1007/BF00970058
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DOI: https://doi.org/10.1007/BF00970058