## Theory and applications of some new classes of integral equations |

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### Contents

INTRODUCTION | 1 |

Investigation of a New Class of Integral | 11 |

Investigation of the Scalar Equations | 35 |

Copyright | |

28 other sections not shown

### Other editions - View all

Theory and Applications of Some New Classes of Integral Equations Alexander G. Ramm Limited preview - 2012 |

Theory and Applications of Some New Classes of Integral Equations Alexander G Ramm No preview available - 1980 |

### Common terms and phrases

analytic Appendix arbitrary shape assume assumptions asymptotic basis of H bodies of arbitrary boundary condition bounded calculated capacitance characteristic values complex poles const defined by formula denote diffraction dipole Dirichlet problem discrete spectrum disk domain eigenfunctions eigenvalues equa equation 1.1 estimate example exp(ikr follows geometric series given Green's formula Green's function Hence Hilbert space holds inequality initial field inner product integral equations invertible iterative process Let us prove linear operator linear span magnetic minimal order nonlinear nonselfadjoint norm obtain one-port operator in H order of singularity orthonormal basis plane polarizability polarizability tensor poles of Green's potential Proof of Theorem Ramm remains to prove Remark Riesz basis root vectors satisfies scattering amplitude scattering matrix Section selfadjoint sequence small bodies smooth solution of equation solve space H subspace sufficiently tensor theory tion unique solution wave scattering