A problem in analysis
Alexander G. Ramm · Analysis · 2012
Assume that D ⊂ ℝ 2 is a bounded domain, diffeomorphic to a disc, star-shaped, with a C 1, λ boundary C , λ > 0 , which can be represented in polar coordinates as r = f ( φ ) , where f > 0 is a smooth 2 π -periodic function. Let ψ ± n : = ψ ± n ( φ ): = e ± in φ f n ( φ ). Theorem. Assume that ∫ 0 2 π ψ ± n f 2 ( φ ) d φ = 0 n = 1, 2,⋯ Then f = const .