This article is cited in 2 papers

Cauchy Problem for Convolution Equations in Spaces of Analytic Vector-Valued Functions

V. P. Gromov

Orel State University

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.

Keywords: operator-differential convolution equation, Cauchy problem, Fourier method, entire function of exponential type, Borel transform, Fourier–Laplace transform.

UDC: 517.55

Received: 19.10.2005
Revised: 11.01.2007

DOI: 10.4213/mzm3798

 English version: Mathematical Notes, 2007, 82:2, 165–173

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