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.
Citation:
V. P. Gromov, “Cauchy Problem for Convolution Equations in Spaces of Analytic Vector-Valued Functions”, Mat. Zametki, 82:2 (2007), 190–200; Math. Notes, 82:2 (2007), 165–173
This publication is cited in the following 2 articles:
L. F. Logacheva, “O differentsialno-operatornykh uravneniyakh v chastnykh proizvodnykh v lokalno vypuklykh prostranstvakh”, Vestnik rossiiskikh universitetov. Matematika, 24:125 (2019), 90–98
S. N. Man'ko, “Vector-valued functions generated by the operator of finite order and their application to solving operator equations in locally convex spaces”, Russian Math. (Iz. VUZ), 62:3 (2018), 34–44