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Complex cauchy problem in the class of analytic functions with integral metric

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Abstract

We study the complex Cauchy problem for a system of linear differential equations in the class of analytic functions with integral metric. In the case of a Hardy-Lebesgue type weighted L p -space, we obtain necessary and sufficient conditions for the local solvability of the problem.

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References

  1. Dubinskii, Yu.A., Zadacha Koshi v kompleksnoi oblasti (Cauchy Problem in Complex Domain), Moscow, 1996.

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  2. Biryukov, A.M., Cauchy Complex Problem in Spaces with Integral Metrics, Vestnik MEI, 2011, no. 6, pp. 126–132.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute,”, Moscow, Russia

    A. M. Biryukov

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  1. A. M. Biryukov
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Dedicated to the jubilee of Vladimir Aleksandrovich Il’in

Original Russian Text © A.M. Biryukov, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 6, pp. 779–783.

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Biryukov, A.M. Complex cauchy problem in the class of analytic functions with integral metric. Diff Equat 49, 750–754 (2013). https://doi.org/10.1134/S0012266113060098

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  • DOI: https://doi.org/10.1134/S0012266113060098

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