Correct answer: (A) D_a is a linear isometry.; (B) D_a is bijective.; (D) D_a is bounded below.
Explanation
Substitute t=x/a to get ‖D_af‖²=∫a⁻¹|f(x/a)|²dx=‖f‖². Thus it is a linear isometry and bounded below with constant 1. Composition gives D_aD_b=D_(ab), so inverse D_(1/a) exists and C is false. **A,B,D**.
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