FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES

INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION

A Kernel Smoothing Method for General Integral Equations |

I. M. Novitskii |

2012, issue 2, P. |

Abstract |

In this paper, we reduce the general linear integral equation of the third kind in $L^2(Y,\mu)$, with largely arbitrary kernel and coefficient, to an equivalent integral equation either of the second kind or of the first kind in $L^2(\mathbb{R})$, with the kernel being the linear pencil of bounded infinitely differentiable bi-Carleman kernels expandable in absolutely and uniformly convergent bilinear series. The reduction is done by using unitary equivalence transformations. |

linear integral equations of the first, second, and third kind, unitary operator, multiplication operator, bi-integral operator, bi-Carleman kernel, Hilbert-Schmidt kernel, bilinear series expansions of kernelsKeywords: |

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## References |

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