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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 190–200 (Mi mz3798)  

This article is cited in 1 scientific paper (total in 1 paper)

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

DOI: https://doi.org/10.4213/mzm3798

Full text: PDF file (443 kB)
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English version:
Mathematical Notes, 2007, 82:2, 165–173

Bibliographic databases:

UDC: 517.55
Received: 19.10.2005
Revised: 11.01.2007

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  isi
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