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Approximate Solutions of One Abstract Cauchy Problem

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We find approximate solutions of the Cauchy problem for a differential-operator equation of hyperbolic type with degeneration in a Hilbert space. In terms of these approximations, we give a characteristic of the Gevrey classes for a nonnegative self-adjoint operator.

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References

  1. A. V. Babin, “Representation of solutions of differential equations in the polynomial form,” Usp. Mat. Nauk, 38, No. 2, 228–229 (1983).

    Google Scholar 

  2. A. V. Babin, “On the polynomial solvability of differential equations with coefficients from the classes of infinitely differentiable functions,” Mat. Zametki, 34, No 2, 249–260 (1983).

    MathSciNet  Google Scholar 

  3. A. V. Babin, “Solution of the Cauchy problem with the help of weight approximations of the exponents by polynomials,” Funkts. Anal. Prilozhen., 17, No. 4, 75–76 (1983).

    Google Scholar 

  4. A. V. Babin, “Construction and investigation of the solutions of differential equations by methods of the theory of approximation of functions,” Mat. Sb., 123, No. 2, 147–174 (1984).

    MathSciNet  MATH  Google Scholar 

  5. M. L. Gorbachuk and V. V. Gorodetskii, “On the solutions of differential equations in Hilbert spaces,” Usp. Mat. Nauk, 39, No. 4, 140 (1984).

    Google Scholar 

  6. V. V. Gorodetskii and M. L. Gorbachuk, “Polynomial approximation of solutions of operator-differential equations in a Hilbert space,” Ukr. Mat. Zh., 36, No. 4, 500–502 (1984); English translation: Ukr. Math. J., 36, No. 4, 409–411 (1984).

  7. P. K. Suetin, Classical Orthogonal Polynomials [in Russia], Nauka, Moscow (1976).

    Google Scholar 

  8. V. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).

    MATH  Google Scholar 

  9. L. I. Vainerman, “Hyperbolic equations with degeneration in Hilbert spaces,” Sib. Mat. Zh., 18, No. 4, 736–746 (1977).

    Google Scholar 

  10. W. B. Caton and E. Hille, “Laguerre polynomials and Laplace integrals,” Duke Math. J., 12, No. 2, 217–242 (1945).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Fedkovych Chernivtsi National University, Kotsyubyns’kyi Str., 2, Chernivtsi, 58012, Ukraine

    V. V. Horodets’kyi & O. V. Martynyuk

Authors
  1. V. V. Horodets’kyi
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  2. O. V. Martynyuk
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Corresponding author

Correspondence to V. V. Horodets’kyi.

Additional information

Translated from Neliniini Kolyvannya, Vol. 22, No. 3, pp. 341–349, July–September, 2019.

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Horodets’kyi, V.V., Martynyuk, O.V. Approximate Solutions of One Abstract Cauchy Problem. J Math Sci 253, 230–241 (2021). https://doi.org/10.1007/s10958-021-05224-6

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  • DOI: https://doi.org/10.1007/s10958-021-05224-6

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