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Spectral synthesis in spaces invariant under composition semigroups

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Abstract

If φt is a continuously differentiable composition semigroup of analytic endomorphisms of the disk\(\mathbb{D}\), then all closed subspaces of Hol(\(\mathbb{D}\)) invariant with respect to this semigroup (acting by compositions) admit spectral synthesis. Bibliography: 11 titles.

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Literature Cited

  1. C. C. Cowen, “Iteration and the solution of functional equations for functions analytic in the unit disk,”Trans. Amer. Math. Soc.,265, No. 1, 69–95 (1981).

    MATH  MathSciNet  Google Scholar 

  2. A. F. Leont'ev, “On summation of Dirichlet series with complex exponent and its application,”Tr. Mat. Inst. Akad. Nauk SSSR,112, 300–326 (1971).

    MATH  MathSciNet  Google Scholar 

  3. A. F. Leont'ev,Sequences of Exponential Polynomials [in Russian], Moscow (1980).

  4. Ch. Pommerenke,Univalent Functions, Vandhoeck&Ruprecht, Göttingen (1975).

    Google Scholar 

  5. P. L. Duren,Univalent Functions, Springer-Verlag (1983).

  6. J.-P. Kahane,Lectures on Mean Periodic Functions, Tata Inst., Bombay (1959).

    Google Scholar 

  7. G. H. Hardy,Divergent Series, Clarendon Press, Oxford (1949).

    Google Scholar 

  8. V. I. Vasyunin and N. K. Nikolskii, “Operator measures and coefficients of univalent functions,”Algebra Analiz 3, No. 6, 1–76 (1991).

    MathSciNet  Google Scholar 

  9. G. M. Goluzin,Geometric Theory of Functions of Complex Variables [in Russian], Moscow (1966).

  10. B. Ya. Levin, “Majorants in some classes of subharmonic functions and their applications. I,” Preprint FTINT, 18-84, Kharkov (1984).

  11. E. Berkson and H. Porta, “Semigroups of analytic functions and composition operators,”Michigan Math. J.,25, No. 1, 101–116 (1978).

    MathSciNet  Google Scholar 

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Authors
  1. I. V. Dondoshanskii
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993, pp. 55–77.

Translated by V. I. Vasyunin.

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Dondoshanskii, I.V. Spectral synthesis in spaces invariant under composition semigroups. J Math Sci 80, 1908–1921 (1996). https://doi.org/10.1007/BF02367005

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  • DOI: https://doi.org/10.1007/BF02367005

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