Regular and Chaotic Dynamics

, Volume 14, Issue 2, pp 248–262 | Cite as

Asymptotic behavior of generalized convolutions

Research Articles

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.

Key words

convolution fixed point Hermite polynomials 

MSC2000 numbers

47B38 45P05 33C45 33C90 

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References

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

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Mathematics DepartmentPrinceton UniversityPrincetonUSA

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