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Journal of Mathematical Sciences

, Volume 128, Issue 2, pp 2822–2824 | Cite as

Integral Equations of Fredholm Type with Rapidly Varying Kernels and Their Relationship to Dynamic Systems

  • S. Yu. Slavyanov
Article
  • 24 Downloads

Abstract

The relationship between the eigenfunctions of a Fredholm-type integral equation with rapidly oscillating kernel and the dynamic mapping is analyzed. Differential operators commuting with the Fourier operator are constructed. These operators are closely related to nontrivial solutions of the unperturbed nonlinear functional equation related to the dynamic mapping. Bibliography: 6 titles.

Keywords

Fourier Dynamic System Integral Equation Functional Equation Differential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

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    V. F. Lazutkin, “Eigenfunctions with given caustic,” Zh. Vychisl. Mat. Mat. Fiz., 10, No.2, 362–373 (1970).Google Scholar
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    S. Yu. Slavyanov, “The construction of the asymptotics of the eigenfunctions of Fredholm type integral equations with symmetric rapidly oscillating kernels,” in: Problems of Mathematical Physics [in Russian], No. 6, Izdat. Leningrad. Univ., Leningrad (1973), pp. 134–141.Google Scholar
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. Yu. Slavyanov
    • 1
  1. 1.Department of Computational PhysicsSt.Petersburg State UniversitySt. PetersburgRussia

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