M is the closed space of even functions, whose orthogonal complement is the odd functions. Split eᵗ=cosh t+sinh t. The distance is ‖sinh t‖₂. Its square is ∫₋₁¹(e²ᵗ+e⁻²ᵗ−2)/4 dt=(e²−e⁻²−4)/4. Taking the square root gives **D**.
More Hilbert Spaces questions
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