Geodesic
Some features of second kind Fredholm equations kernels
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 28-33

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Kernels of Fredholm integral equations of the second kind with exceptions are analysed in this article. The equations under consideration have a meaning of magnetic field boundary condition and are used in problems of scattering on scatterers with finite thickness. It is shown that these kernels could be stated in a form of Dirac delta-functions. This mathematical formalization results in interesting physical effect that induced current calculated via physical optics equals the difference of face and back currents of the scatterer, calculated using method of integral equations.
Keywords: integral equations, scattering problem for electromagnetic fields, Dirac delta function. 
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     author = {M. A. Buzova},
     title = {Some features of second kind {Fredholm} equations kernels},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {28--33},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a3/}
}
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M. A. Buzova. Some features of second kind Fredholm equations kernels. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 28-33. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a3/