How do I show $\|(e^{-2\pi ihx} - 1)/h \| \leq 2 \pi \|x\|$? for each h and x? I thought about using taylor expansion of Euler's formula, but it did not work out. Thank you in advance.
How do I show $\|(e^{-2\pi ihx_j} - 1)/h \| \leq 2 \pi \|x\|$?
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complex-analysis
inequality