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Investigation of a New Class of Integral
Investigation of the Scalar Equations
28 other sections not shown
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