Let $P$ be a projection defined on $L_2(\mathbb{R})$ by multiplying with the function of value $1$ for $-1
Is the following operator a projection?
2
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functional-analysis
fourier-analysis
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2This cannot be a projection. The FT of a function with compact support has unbounded support, and likewise for the inverse FT. Thus every time your operator is applied, the signal is clipped in the frequency domain, and thus the signal is changed. – 2011-05-15