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A Pair of Dual Integral Equations Occurring in Diffraction Theory

1962
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Proceedings of the Edinburgh Mathematical Society
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Dual integral equations of the form f 00f Jo where f(x) and g(x) are given functions, \j/(x) is unknown, k^.0, \i, v and a are real constants, have applications to diffraction theory and also to dynamical problems in elasticity. The special cases v = -\i, a = 0 and v = n = 0, 0 < a 2 < l were treated by Ahiezer (1). More recently, equations equivalent to the above were solved by Peters (2) who adapted a method used earlier by Gordon (3) for treating the (extensively studied) case /x = v, k = 0.

doi:10.1017/s0013091500014784
fatcat:vmjyxknhyjgefbkun2renf65mu