We study an optimization problem arising in antenna theory: that of finding square integrable currents (boundary data) of norm 1 on an arbitrary surface which optimize the power radiated in a preassigned angular sector. Specifically we develop a constructive method using complete families of solutions of the exterior Helmholtz equation, which produces approximately optimal boundary data in terms of solutions of a generalized eigenvalue problem Bx = λ Gx. Convergence of an appropriate subsequence of approximate currents to the optimal current is established.
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Angell et al. (1984) studied this question.
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