Geodesic
Cauchy Problem for Convolution Equations in Spaces of Analytic Vector-Valued Functions
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 190-200

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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.
Keywords: operator-differential convolution equation, Cauchy problem, Fourier method, entire function of exponential type
Mots-clés : Borel transform, Fourier–Laplace transform. 
@article{MZM_2007_82_2_a3,
     author = {V. P. Gromov},
     title = {Cauchy {Problem} for {Convolution} {Equations} in {Spaces} of {Analytic} {Vector-Valued} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {190--200},
     publisher = {mathdoc},
     volume = {82},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a3/}
}
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V. P. Gromov. Cauchy Problem for Convolution Equations in Spaces of Analytic Vector-Valued Functions. Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 190-200. http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a3/