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Area Measure and Orthogonal Vectors

Let m be an area measure on {z in C:|z| < 1}.
Show that 1, z, z^2,... are orthogonal vectors in L^2(m).
Find ||z^n||, n >= 0.
If e_n=(z^n)/||z^n||, n >= 0, is {e_0, e_1,...} a basis for L^2(m)?

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