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Asymptotic behavior of generalized convolutions

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Abstract

We study the behavior of a class of convolution-type nonlinear transformations. Under some smallness conditions we prove the existence of fixed points and analyze the spectrum of the associated linearized operator.

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References

  1. Li, D. and Sinai, Ya.G., Blow Ups of Complex Solutions of the 3D-Navier-Stokes System and Renormalization Group Method, J. Eur. Math. Soc., 2008, vol. 10, no. 2, pp. 267–313.

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  2. Li, D. and Sinai, Ya.G., Complex Singularities of the Burgers System and Renormalization Group Method, in Current Developments in Mathematics, 2006, International Press, 2008, pp. 181–210.

  3. Reed, M. and Simon, B., Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press, 1972.

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Correspondence to D. Li.

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Li, D., Sinai, Y.G. Asymptotic behavior of generalized convolutions. Regul. Chaot. Dyn. 14, 248–262 (2009). https://doi.org/10.1134/S1560354709020051

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  • DOI: https://doi.org/10.1134/S1560354709020051

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