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Let  B  be a subalgebra of      L ∞  {L^\infty }       containing      H ∞  {H^\infty }      . We give some necessary and sufficient conditions, expressed in terms of analyticity, for a function in      L ∞  {L^\infty }       to belong to  B .

Analyticity of functions and subalgebras of 𝐿^{∞} containing 𝐻^{∞}