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Polynomial approximations of solutions of higher-order operator-differential equations

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Abstract

We study the Cauchy problem for higher-order operator-differential equations in a Banach space and construct polynomial approximations of its solutions.

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References

  1. S. Ya. Yakubov,Linear Operator-Differential Equations and Their Applications [in Russian], Nauka, Baku (1985).

    Google Scholar 

  2. V. V. Gorodetskii and M. L. Gorbachuk, “Polynomial approximations to solutions of operator-differential equations in Hilbert spaces,”Ukr. Mat. Zh.,36, No. 4, 500–502 (1984).

    Google Scholar 

  3. A. V. Babin, “Construction and investigation of solutions of differential equations by the methods of the theory of approximation of functions,”Mat. Sb.,123, No. 2, 147–173 (1984).

    Google Scholar 

  4. J. Goldstein,Semigroups of Linear Operators and Their Applications [Russian translation], Vyshcha Shkola, Kiev (1989).

    Google Scholar 

  5. V. I. Gorbachuk and A. V. Knyazyuk, “Boundary values of solutions of operator-differential equations,”Usp. Mat. Nauk,44, No. 3, 55–91 (1989).

    Google Scholar 

  6. V. V. Vasil'ev, S. G. Krein, and S. I. Piskarev, “Semigroups of operators, cosine operator functions, and linear differential equations,” in:VINITI Series in Mathematical Analysis [in Russian], Vol. 28, VINITI, Moscow (1990), pp. 87–202.

    Google Scholar 

  7. A. V. Babin, “Representation of solutions of differential equations in terms of iterations of differential operators,”Mat. Sb.,105 (147), No. 3, 467–484 (1978).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 952–955, July, 1994.

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Orudzhev, G.D. Polynomial approximations of solutions of higher-order operator-differential equations. Ukr Math J 46, 1045–1048 (1994). https://doi.org/10.1007/BF01056683

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  • DOI: https://doi.org/10.1007/BF01056683

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