What does " $\sup_{n \geq 1} |f_n|^2$ is summable" mean?
Question on Notation (with respect to a sequence of functions)
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analysis
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0Being "summable" means that $\sum_{k = 1}^\infty |f(k)|<\infty$. So, if $\hat{f} = \sup_{n\geq 1}|f_n|^2$, this is just saying that $\sum_{k = 1}^\infty |\hat{f}(k)|<\infty$. – 2017-01-19
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2No, "summable" is usually meant as a synonym for "Lebesgue integrable" (on whatever domain is being considered). – 2017-01-19
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0Alright, that makes sense. Thanks! – 2017-01-19