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Cauchy problem for convolution equations in spaces of analytic vector-valued functions

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Abstract

The present paper is devoted to the Cauchy problem of inhomogeneous convolution equations of a fairly general nature. To solve the problems posed here, we apply the operator method proposed in some earlier papers by the author. The solutions of the problems under consideration are found using an effective method in the form of well-convergent vector-valued power series. The proposed method ensures the continuity of the obtained solutions with respect to the initial data and the inhomogeneous term of the equation.

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References

  1. M. Lax, Fluctuation and Coherence Phenomena in Classical and Quantum Physics (Gordon and Breach, New York, 1968).

    Google Scholar 

  2. V. P. Gromov, “Analytic solutions of operator-differential equations in locally convex spaces,” Dokl. Ross. Akad. Nauk 394 (3), 305–308 (2004).

    MathSciNet  Google Scholar 

  3. V. P. Gromov, “An operator method for solving linear equations,” in Uchenye Zapiski OGU (Orel, 2002), Vol. 3, pp. 4–36 [in Russian].

    Google Scholar 

  4. F. Trèves, Ovcyanikov Theorem and Hyperdifferential Operators, in Notas de Matemática (Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968), Vol. 46.

    Google Scholar 

  5. S. Steinberg, “The Cauchy problem for differential equations of infinite order,” J. Differential Equations 9 (3), 591–607(1971).

    Article  MATH  MathSciNet  Google Scholar 

  6. L. V. Ovsyannikov, “A singular operator on the scale of Banach spaces,” Dokl. Akad. Nauk SSSR 163, 819–822 (1965) [Soviet Math. Dokl. 6, 1025–1028 (1965)].

    MathSciNet  Google Scholar 

  7. A. O. Gel’fond and A. F. Leont’ev, “On a generalization of the Fourier series,” Mat. Sb. 29 (71) (3), 477–500 (1951).

    MathSciNet  Google Scholar 

  8. V. P. Gromov, “The order and type of a linear operator and entire vector-valued function,” in Uchenye Zapiski OGU (Orel, 1999), Vol. 1, pp. 6–23 [in Russian].

    MathSciNet  Google Scholar 

  9. A. F. Leont’ev, Generalizations of Exponential Series (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  10. L. Hörmander, An Introduction to Complex Analysis in Several Variables (Van Nostrand, Princeton, NJ,-Toronto, Ont.,-London, 1966; Mir, Moscow, 1968).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Orlov State University, USA

    V. P. Gromov

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  1. V. P. Gromov
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Gromov, V.P. Cauchy problem for convolution equations in spaces of analytic vector-valued functions. Math Notes 82, 165–173 (2007). https://doi.org/10.1134/S0001434607070218

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  • DOI: https://doi.org/10.1134/S0001434607070218

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