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Analyticity of extremizers to the Airy-Strichartz inequality
We prove that there exists an extremal function to the Airy–Strichartz inequality ‖ e − t ∂ x 3 f ‖ L t , x 8 ( ℝ × ℝ ) ⩽ C ‖ f ‖ L 2 ( ℝ ) , using the linear profile decomposition. Furthermore we show …